{"segments": [{"id": 1, "seek": 2291, "start": 11.85, "end": 22.91, "text": " Inshallah we'll start numerical descriptive majors for the population. Last time we talked about the same majors.", "tokens": [682, 2716, 13492, 321, 603, 722, 29054, 42585, 31770, 337, 264, 4415, 13, 5264, 565, 321, 2825, 466, 264, 912, 31770, 13], "avg_logprob": -0.3590353364529817, "compression_ratio": 1.175257731958763, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 11.85, "end": 12.69, "word": " Inshallah", "probability": 0.6461588541666666}, {"start": 12.69, "end": 12.91, "word": " we'll", "probability": 0.5450439453125}, {"start": 12.91, "end": 13.33, "word": " start", "probability": 0.92724609375}, {"start": 13.33, "end": 14.09, "word": " numerical", "probability": 0.55029296875}, {"start": 14.09, "end": 15.07, "word": " descriptive", "probability": 0.66552734375}, {"start": 15.07, "end": 16.37, "word": " majors", "probability": 0.340576171875}, {"start": 16.37, "end": 16.89, "word": " for", "probability": 0.9267578125}, {"start": 16.89, "end": 17.17, "word": " the", "probability": 0.30712890625}, {"start": 17.17, "end": 17.77, "word": " population.", "probability": 0.7412109375}, {"start": 18.87, "end": 19.11, "word": " Last", "probability": 0.849609375}, {"start": 19.11, "end": 19.37, "word": " time", "probability": 0.8916015625}, {"start": 19.37, "end": 19.65, "word": " we", "probability": 0.8369140625}, {"start": 19.65, "end": 20.51, "word": " talked", "probability": 0.88330078125}, {"start": 20.51, "end": 20.93, "word": " about", "probability": 0.90625}, {"start": 20.93, "end": 22.27, "word": " the", "probability": 0.91357421875}, {"start": 22.27, "end": 22.51, "word": " same", "probability": 0.90283203125}, {"start": 22.51, "end": 22.91, "word": " majors.", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 2, "seek": 4314, "start": 24.2, "end": 43.14, "text": " I mean the same descriptive measures for a sample. And we have already talked about the mean, variance, and standard deviation. These are called statistics because they are computed from the sample. 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So descriptive statistics described previously in the last two lectures was for a sample. Here we'll just see how can we compute these measures for the entire population. 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A statistic is a value that computed from a sample, but parameter is a value computed from population. So the important population parameters are population mean, variance, and standard deviation.", "tokens": [400, 498, 291, 1604, 264, 700, 7991, 11, 321, 848, 456, 307, 257, 2649, 1296, 12523, 293, 9834, 13, 316, 29588, 307, 257, 2158, 300, 40610, 490, 257, 6889, 11, 457, 13075, 307, 257, 2158, 40610, 490, 4415, 13, 407, 264, 1021, 4415, 9834, 366, 4415, 914, 11, 21977, 11, 293, 3832, 25163, 13], "avg_logprob": -0.21051136526194486, "compression_ratio": 1.7705882352941176, "no_speech_prob": 0.0, "words": [{"start": 75.14, "end": 75.94, "word": " And", "probability": 0.650390625}, {"start": 75.94, "end": 76.08, "word": " if", "probability": 0.90283203125}, {"start": 76.08, "end": 76.16, "word": " you", "probability": 0.96240234375}, {"start": 76.16, "end": 76.46, "word": " remember", "probability": 0.869140625}, {"start": 76.46, "end": 76.94, "word": " the", "probability": 0.322509765625}, {"start": 76.94, "end": 77.2, "word": " first", "probability": 0.88232421875}, {"start": 77.2, "end": 77.54, "word": " lecture,", "probability": 0.93310546875}, {"start": 77.66, "end": 77.72, "word": " we", "probability": 0.92138671875}, {"start": 77.72, "end": 77.92, "word": " said", "probability": 0.91015625}, {"start": 77.92, "end": 78.12, "word": " there", "probability": 0.85595703125}, {"start": 78.12, "end": 78.32, "word": " is", "probability": 0.818359375}, {"start": 78.32, "end": 78.56, "word": " a", "probability": 0.8388671875}, {"start": 78.56, "end": 79.2, "word": " difference", "probability": 0.496826171875}, {"start": 79.2, "end": 79.8, "word": " between", "probability": 0.85009765625}, {"start": 79.8, "end": 80.96, "word": " statistics", "probability": 0.896484375}, {"start": 80.96, "end": 81.86, "word": " and", "probability": 0.9404296875}, {"start": 81.86, "end": 82.34, "word": " parameters.", "probability": 0.94921875}, {"start": 83.08, "end": 83.26, "word": " A", "probability": 0.381591796875}, {"start": 83.26, "end": 83.64, "word": " statistic", "probability": 0.8935546875}, {"start": 83.64, "end": 83.88, "word": " is", "probability": 0.9462890625}, {"start": 83.88, "end": 84.02, "word": " a", "probability": 0.9853515625}, {"start": 84.02, "end": 84.3, "word": " value", "probability": 0.95556640625}, {"start": 84.3, "end": 84.54, "word": " that", "probability": 0.9189453125}, {"start": 84.54, "end": 84.98, "word": " computed", "probability": 0.488037109375}, {"start": 84.98, "end": 85.28, "word": " from", "probability": 0.8486328125}, {"start": 85.28, "end": 85.44, "word": " a", "probability": 0.57470703125}, {"start": 85.44, "end": 85.78, "word": " sample,", "probability": 0.5908203125}, {"start": 86.4, "end": 86.64, "word": " but", "probability": 0.80615234375}, {"start": 86.64, "end": 87.12, "word": " parameter", "probability": 0.5625}, {"start": 87.12, "end": 87.42, "word": " is", "probability": 0.9423828125}, {"start": 87.42, "end": 87.52, "word": " a", "probability": 0.93359375}, {"start": 87.52, "end": 87.68, "word": " value", "probability": 0.96142578125}, {"start": 87.68, "end": 88.14, "word": " computed", "probability": 0.904296875}, {"start": 88.14, "end": 88.5, "word": " from", "probability": 0.88037109375}, {"start": 88.5, "end": 88.98, "word": " population.", "probability": 0.87841796875}, {"start": 89.82, "end": 90.44, "word": " So", "probability": 0.94677734375}, {"start": 90.44, "end": 91.38, "word": " the", "probability": 0.57958984375}, {"start": 91.38, "end": 92.14, "word": " important", "probability": 0.88916015625}, {"start": 92.14, "end": 93.44, "word": " population", "probability": 0.96142578125}, {"start": 93.44, "end": 94.0, "word": " parameters", "probability": 0.96630859375}, {"start": 94.0, "end": 95.68, "word": " are", "probability": 0.9208984375}, {"start": 95.68, "end": 96.64, "word": " population", "probability": 0.943359375}, {"start": 96.64, "end": 97.02, "word": " mean,", "probability": 0.88720703125}, {"start": 97.66, "end": 98.56, "word": " variance,", "probability": 0.87890625}, {"start": 98.98, "end": 99.6, "word": " and", "probability": 0.94482421875}, {"start": 99.6, "end": 100.44, "word": " standard", "probability": 0.935546875}, {"start": 100.44, "end": 101.64, "word": " deviation.", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 5, "seek": 12686, "start": 102.68, "end": 126.86, "text": " Let's start with the first one, the mean, or the population mean. As the sample mean is defined by the sum of the values divided by the sample size. But here, we have to divide by the population size. So that's the difference between sample mean and population mean. For the sample mean, we use x bar.", "tokens": [961, 311, 722, 365, 264, 700, 472, 11, 264, 914, 11, 420, 264, 4415, 914, 13, 1018, 264, 6889, 914, 307, 7642, 538, 264, 2408, 295, 264, 4190, 6666, 538, 264, 6889, 2744, 13, 583, 510, 11, 321, 362, 281, 9845, 538, 264, 4415, 2744, 13, 407, 300, 311, 264, 2649, 1296, 6889, 914, 293, 4415, 914, 13, 1171, 264, 6889, 914, 11, 321, 764, 2031, 2159, 13], "avg_logprob": -0.15930707212807477, "compression_ratio": 1.776470588235294, "no_speech_prob": 0.0, "words": [{"start": 102.68, "end": 103.06, "word": " Let's", "probability": 0.83935546875}, {"start": 103.06, "end": 103.4, "word": " start", "probability": 0.9296875}, {"start": 103.4, "end": 103.56, "word": " with", "probability": 0.90283203125}, {"start": 103.56, "end": 103.68, "word": " the", "probability": 0.91748046875}, {"start": 103.68, "end": 103.94, "word": " first", "probability": 0.861328125}, {"start": 103.94, "end": 104.24, "word": " one,", "probability": 0.92236328125}, {"start": 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This is pronounced as mu. So mu is the sum of the x values divided by the population size, not the sample size. So it's quite similar to the sample mean. So mu is the population mean, n is the population size, and xi is the it value of the variable x. 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Here, we subtract the population mean instead of the sample mean. So sum of xi minus mu squared, then divide by this population size, capital N, instead of N minus 1. 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Here, we subtract the mean of the population, mu, then divide by capital N instead of N minus 1. So the computations for the sample and the population mean or variance are quite similar. 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The population variance is denoted by sigma squared. And finally, the population standard deviation is denoted by sigma. So that's the numerical descriptive measures either for a sample or a population. 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On the other hand, for the sample statistics, we have x bar for sample mean, s squared for the sample variance, and s is the sample standard deviation. 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Let's move to new topic, which is empirical role. Now, empirical role is just we have to approximate the variation of data in case of", "tokens": [2639, 1168, 30, 961, 311, 1286, 281, 777, 4829, 11, 597, 307, 31886, 3090, 13, 823, 11, 31886, 3090, 307, 445, 321, 362, 281, 30874, 264, 12990, 295, 1412, 294, 1389, 295], "avg_logprob": -0.19874526515151514, "compression_ratio": 1.2758620689655173, "no_speech_prob": 0.0, "words": [{"start": 305.1, "end": 305.36, "word": " Any", "probability": 0.8330078125}, {"start": 305.36, "end": 305.7, "word": " question?", "probability": 0.57373046875}, {"start": 310.94, "end": 311.78, "word": " Let's", "probability": 0.825439453125}, {"start": 311.78, "end": 312.2, "word": " move", "probability": 0.94775390625}, {"start": 312.2, "end": 312.6, "word": " to", "probability": 0.91845703125}, {"start": 312.6, "end": 312.8, "word": " new", "probability": 0.62744140625}, {"start": 312.8, "end": 313.02, "word": " topic,", "probability": 0.99169921875}, {"start": 314.32, "end": 314.96, "word": " which", "probability": 0.95751953125}, {"start": 314.96, "end": 315.88, "word": " is", "probability": 0.9521484375}, {"start": 315.88, "end": 316.86, "word": " empirical", "probability": 0.8046875}, {"start": 316.86, "end": 317.24, "word": " role.", "probability": 0.51708984375}, {"start": 319.34, "end": 320.18, "word": " Now,", "probability": 0.94873046875}, {"start": 320.24, "end": 320.54, "word": " empirical", "probability": 0.8701171875}, {"start": 320.54, "end": 321.02, "word": " role", "probability": 0.93798828125}, {"start": 321.02, "end": 321.88, "word": " is", "probability": 0.89794921875}, {"start": 321.88, "end": 322.3, "word": " just", "probability": 0.91943359375}, {"start": 322.3, "end": 325.62, "word": " we", "probability": 0.427490234375}, {"start": 325.62, "end": 326.0, "word": " have", "probability": 0.95166015625}, {"start": 326.0, "end": 326.16, "word": " to", "probability": 0.9765625}, {"start": 326.16, "end": 326.74, "word": " approximate", "probability": 0.8837890625}, {"start": 326.74, "end": 327.14, "word": " the", "probability": 0.89697265625}, {"start": 327.14, "end": 327.52, "word": " variation", "probability": 0.9267578125}, {"start": 327.52, "end": 327.78, "word": " of", "probability": 0.95751953125}, {"start": 327.78, "end": 328.16, "word": " data", "probability": 0.9345703125}, {"start": 328.16, "end": 329.74, "word": " in", "probability": 0.88525390625}, {"start": 329.74, "end": 330.12, "word": " case", "probability": 0.919921875}, {"start": 330.12, "end": 330.62, "word": " of", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 14, "seek": 34537, "start": 331.15, "end": 345.37, "text": " They'll shift. I mean suppose the data is symmetric around the mean. 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I mean, the mean, the area to the right of the mean equals 50%, which is the same as the area to the left of the mean. Now suppose or consider the data is bell-shaped. Bell-shaped, normal, or symmetric? So it's not skewed either to the right or to the left. So here we assume, okay, the data is bell-shaped. 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Number one, approximately 68% of the data in a bill shipped lies within one standard deviation of the population. So this is the first rule, 68% of the data or of the observations", "tokens": [1219, 23317, 11, 13420, 11, 11803, 13, 22, 4978, 13, 5118, 472, 11, 10447, 23317, 4, 295, 264, 1412, 294, 257, 2961, 25312, 9134, 1951, 472, 3832, 25163, 295, 264, 4415, 13, 407, 341, 307, 264, 700, 4978, 11, 23317, 4, 295, 264, 1412, 420, 295, 264, 18163], "avg_logprob": -0.19403698493023308, "compression_ratio": 1.4206896551724137, "no_speech_prob": 0.0, "words": [{"start": 374.18, "end": 374.74, "word": " called", "probability": 0.67919921875}, {"start": 374.74, "end": 375.82, "word": " 68,", "probability": 0.90087890625}, {"start": 376.18, "end": 377.76, "word": " 95,", "probability": 0.52685546875}, {"start": 378.16, "end": 378.54, "word": " 99", "probability": 0.9658203125}, {"start": 378.54, "end": 379.16, "word": ".7", "probability": 0.977783203125}, {"start": 379.16, "end": 379.5, "word": " rule.", "probability": 0.6552734375}, {"start": 380.96, "end": 381.8, "word": " Number", "probability": 0.8642578125}, {"start": 381.8, "end": 382.1, "word": " one,", "probability": 0.87451171875}, {"start": 382.96, "end": 383.54, "word": " approximately", "probability": 0.82861328125}, {"start": 383.54, "end": 384.06, "word": " 68", "probability": 0.96044921875}, {"start": 384.06, "end": 384.48, "word": "%", "probability": 0.410888671875}, {"start": 384.48, "end": 384.62, "word": " of", "probability": 0.97265625}, {"start": 384.62, "end": 384.76, "word": " the", "probability": 0.8642578125}, {"start": 384.76, "end": 385.18, "word": " data", "probability": 0.9521484375}, {"start": 385.18, "end": 385.6, "word": " in", "probability": 0.92919921875}, {"start": 385.6, "end": 385.72, "word": " a", "probability": 0.98388671875}, {"start": 385.72, "end": 385.86, "word": " bill", "probability": 0.370849609375}, {"start": 385.86, "end": 386.3, "word": " shipped", "probability": 0.77392578125}, {"start": 386.3, "end": 388.48, "word": " lies", "probability": 0.869140625}, {"start": 388.48, "end": 388.96, "word": " within", "probability": 0.91552734375}, {"start": 388.96, "end": 389.86, "word": " one", "probability": 0.927734375}, {"start": 389.86, "end": 390.3, "word": " standard", "probability": 0.9443359375}, {"start": 390.3, "end": 390.74, "word": " deviation", "probability": 0.93115234375}, {"start": 390.74, "end": 391.6, "word": " of", "probability": 0.9677734375}, {"start": 391.6, "end": 391.78, "word": " the", "probability": 0.91796875}, {"start": 391.78, "end": 392.22, "word": " population.", "probability": 0.96484375}, {"start": 394.0, "end": 394.84, "word": " So", "probability": 0.89208984375}, {"start": 394.84, "end": 394.98, "word": " this", "probability": 0.83203125}, {"start": 394.98, "end": 395.08, "word": " is", "probability": 0.9296875}, {"start": 395.08, "end": 395.16, "word": " the", "probability": 0.87939453125}, {"start": 395.16, "end": 395.44, "word": " first", "probability": 0.8828125}, {"start": 395.44, "end": 395.68, "word": " rule,", "probability": 0.86181640625}, {"start": 395.8, "end": 396.16, "word": " 68", "probability": 0.984375}, {"start": 396.16, "end": 396.62, "word": "%", "probability": 0.99267578125}, {"start": 396.62, "end": 396.98, "word": " of", "probability": 0.95166015625}, {"start": 396.98, "end": 397.1, "word": " the", "probability": 0.91552734375}, {"start": 397.1, "end": 397.46, "word": " data", "probability": 0.9462890625}, {"start": 397.46, "end": 399.68, "word": " or", "probability": 0.564453125}, {"start": 399.68, "end": 400.0, "word": " of", "probability": 0.943359375}, {"start": 400.0, "end": 400.14, "word": " the", "probability": 0.91064453125}, {"start": 400.14, "end": 400.76, "word": " observations", "probability": 0.802734375}], "temperature": 1.0}, {"id": 17, "seek": 42860, "start": 401.76, "end": 428.6, "text": " Lie within a mu minus sigma and a mu plus sigma. That's the meaning of the data in bell shape distribution is within one standard deviation of mean or mu plus or minus sigma. 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So 68% of the data. So this is the first rule. 68% of the data lies between mu minus sigma and mu plus sigma.", "tokens": [9134, 1951, 472, 3832, 25163, 295, 264, 914, 11, 2139, 2507, 420, 3673, 309, 13, 407, 23317, 4, 295, 264, 1412, 13, 407, 341, 307, 264, 700, 4978, 13, 23317, 4, 295, 264, 1412, 9134, 1296, 2992, 3175, 12771, 293, 2992, 1804, 12771, 13], "avg_logprob": -0.17491319974263508, "compression_ratio": 1.4603174603174602, "no_speech_prob": 0.0, "words": [{"start": 430.33, "end": 430.81, "word": " lies", "probability": 0.260498046875}, {"start": 430.81, "end": 431.23, "word": " within", "probability": 0.89453125}, {"start": 431.23, "end": 432.21, "word": " one", "probability": 0.85595703125}, {"start": 432.21, "end": 432.69, "word": " standard", "probability": 0.93115234375}, {"start": 432.69, "end": 433.21, "word": " deviation", "probability": 0.904296875}, {"start": 433.21, "end": 434.23, "word": " of", "probability": 0.9296875}, {"start": 434.23, "end": 434.41, "word": " the", "probability": 0.92236328125}, {"start": 434.41, "end": 434.61, "word": " mean,", "probability": 0.96142578125}, {"start": 435.05, "end": 435.33, "word": " either", "probability": 0.90478515625}, {"start": 435.33, "end": 435.77, "word": " below", "probability": 0.8984375}, {"start": 435.77, "end": 436.25, "word": " or", "probability": 0.92919921875}, {"start": 436.25, "end": 436.45, "word": " above", "probability": 0.9794921875}, {"start": 436.45, "end": 436.81, "word": " it.", "probability": 0.9521484375}, {"start": 437.33, "end": 437.59, "word": " So", "probability": 0.583984375}, {"start": 437.59, "end": 437.93, "word": " 68", "probability": 0.7822265625}, {"start": 437.93, "end": 438.25, "word": "%", "probability": 0.8642578125}, {"start": 438.25, "end": 438.95, "word": " of", "probability": 0.953125}, {"start": 438.95, "end": 439.11, "word": " the", "probability": 0.91748046875}, {"start": 439.11, "end": 439.43, "word": " data.", "probability": 0.9580078125}, {"start": 440.15, "end": 440.71, "word": " So", "probability": 0.84521484375}, {"start": 440.71, "end": 440.89, "word": " this", "probability": 0.84033203125}, {"start": 440.89, "end": 441.31, "word": " is", "probability": 0.87890625}, {"start": 441.31, "end": 441.45, "word": " the", "probability": 0.92041015625}, {"start": 441.45, "end": 441.71, "word": " first", "probability": 0.86962890625}, {"start": 441.71, "end": 442.09, "word": " rule.", "probability": 0.90771484375}, {"start": 449.05, "end": 449.81, "word": " 68", "probability": 0.92822265625}, {"start": 449.81, "end": 451.21, "word": "%", "probability": 0.9736328125}, {"start": 451.21, "end": 451.63, "word": " of", "probability": 0.91845703125}, {"start": 451.63, "end": 451.77, "word": " the", "probability": 0.90966796875}, {"start": 451.77, "end": 452.01, "word": " data", "probability": 0.95361328125}, {"start": 452.01, "end": 452.39, "word": " lies", "probability": 0.93310546875}, {"start": 452.39, "end": 453.39, "word": " between", "probability": 0.88671875}, {"start": 453.39, "end": 453.67, "word": " mu", "probability": 0.615234375}, {"start": 453.67, "end": 453.95, "word": " minus", "probability": 0.9609375}, {"start": 453.95, "end": 454.27, "word": " sigma", "probability": 0.908203125}, {"start": 454.27, "end": 454.67, "word": " and", "probability": 0.93896484375}, {"start": 454.67, "end": 457.17, "word": " mu", "probability": 0.89892578125}, {"start": 457.17, "end": 457.43, "word": " plus", "probability": 0.9462890625}, {"start": 457.43, "end": 457.75, "word": " sigma.", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 19, "seek": 48962, "start": 460.48, "end": 489.62, "text": " The other rule is approximately 95% of the data in a bell-shaped distribution lies within two standard deviations of the mean. That means this area covers between minus two sigma and plus mu plus two sigma. So 95% of the data lies between minus mu two sigma", "tokens": [440, 661, 4978, 307, 10447, 13420, 4, 295, 264, 1412, 294, 257, 4549, 12, 23103, 7316, 9134, 1951, 732, 3832, 31219, 763, 295, 264, 914, 13, 663, 1355, 341, 1859, 10538, 1296, 3175, 732, 12771, 293, 1804, 2992, 1804, 732, 12771, 13, 407, 13420, 4, 295, 264, 1412, 9134, 1296, 3175, 2992, 732, 12771], "avg_logprob": -0.14999999837441877, "compression_ratio": 1.6226415094339623, "no_speech_prob": 0.0, "words": [{"start": 460.48, "end": 460.64, "word": " The", "probability": 0.86474609375}, {"start": 460.64, "end": 460.94, "word": " other", "probability": 0.89990234375}, {"start": 460.94, "end": 461.24, "word": " rule", "probability": 0.9013671875}, {"start": 461.24, "end": 461.64, "word": " is", "probability": 0.953125}, {"start": 461.64, "end": 463.96, "word": " approximately", "probability": 0.73681640625}, {"start": 463.96, "end": 464.42, "word": " 95", "probability": 0.974609375}, {"start": 464.42, "end": 464.8, "word": "%", "probability": 0.8779296875}, {"start": 464.8, "end": 465.0, "word": " of", "probability": 0.96142578125}, {"start": 465.0, "end": 465.12, "word": " the", "probability": 0.9111328125}, {"start": 465.12, "end": 465.48, "word": " data", "probability": 0.951171875}, {"start": 465.48, "end": 466.26, "word": " in", "probability": 0.90380859375}, {"start": 466.26, "end": 466.38, "word": " a", "probability": 0.93115234375}, {"start": 466.38, "end": 466.54, "word": " bell", "probability": 0.292724609375}, {"start": 466.54, "end": 466.78, "word": "-shaped", "probability": 0.736328125}, {"start": 466.78, "end": 467.54, "word": " distribution", "probability": 0.869140625}, {"start": 467.54, "end": 468.44, "word": " lies", "probability": 0.81591796875}, {"start": 468.44, "end": 468.7, "word": " within", "probability": 0.79541015625}, {"start": 468.7, "end": 468.98, "word": " two", "probability": 0.9052734375}, {"start": 468.98, "end": 469.38, "word": " standard", "probability": 0.92724609375}, {"start": 469.38, "end": 469.9, "word": " deviations", "probability": 0.931884765625}, {"start": 469.9, "end": 470.2, "word": " of", "probability": 0.9677734375}, {"start": 470.2, "end": 470.34, "word": " the", "probability": 0.93115234375}, {"start": 470.34, "end": 470.52, "word": " mean.", "probability": 0.9775390625}, {"start": 471.08, "end": 471.48, "word": " That", "probability": 0.9111328125}, {"start": 471.48, "end": 471.8, "word": " means", "probability": 0.927734375}, {"start": 471.8, "end": 473.24, "word": " this", "probability": 0.90966796875}, {"start": 473.24, "end": 473.64, "word": " area", "probability": 0.90185546875}, {"start": 473.64, "end": 475.32, "word": " covers", "probability": 0.84716796875}, {"start": 475.32, "end": 478.02, "word": " between", "probability": 0.8798828125}, {"start": 478.02, "end": 478.82, "word": " minus", "probability": 0.9150390625}, {"start": 478.82, "end": 479.52, "word": " two", "probability": 0.489501953125}, {"start": 479.52, "end": 479.88, "word": " sigma", "probability": 0.869140625}, {"start": 479.88, "end": 480.18, "word": " and", "probability": 0.9169921875}, {"start": 480.18, "end": 480.6, "word": " plus", "probability": 0.794921875}, {"start": 480.6, "end": 480.88, "word": " mu", "probability": 0.53955078125}, {"start": 480.88, "end": 481.14, "word": " plus", "probability": 0.94921875}, {"start": 481.14, "end": 481.36, "word": " two", "probability": 0.8935546875}, {"start": 481.36, "end": 481.6, "word": " sigma.", "probability": 0.9208984375}, {"start": 482.64, "end": 483.38, "word": " So", "probability": 0.9580078125}, {"start": 483.38, "end": 483.78, "word": " 95", "probability": 0.89697265625}, {"start": 483.78, "end": 484.14, "word": "%", "probability": 0.9931640625}, {"start": 484.14, "end": 485.9, "word": " of", "probability": 0.96240234375}, {"start": 485.9, "end": 486.04, "word": " the", "probability": 0.919921875}, {"start": 486.04, "end": 486.42, "word": " data", "probability": 0.94580078125}, {"start": 486.42, "end": 487.92, "word": " lies", "probability": 0.9150390625}, {"start": 487.92, "end": 488.36, "word": " between", "probability": 0.87841796875}, {"start": 488.36, "end": 488.88, "word": " minus", "probability": 0.98486328125}, {"start": 488.88, "end": 489.1, "word": " mu", "probability": 0.84814453125}, {"start": 489.1, "end": 489.26, "word": " two", "probability": 0.63037109375}, {"start": 489.26, "end": 489.62, "word": " sigma", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 20, "seek": 51899, "start": 490.59, "end": 518.99, "text": " And finally, approximately 99.7% of the data, it means almost the data. Because we are saying 99.7 means most of the data falls or lies within three standard deviations of the mean. So 99.7% of the data lies between mu minus", "tokens": [400, 2721, 11, 10447, 11803, 13, 22, 4, 295, 264, 1412, 11, 309, 1355, 1920, 264, 1412, 13, 1436, 321, 366, 1566, 11803, 13, 22, 1355, 881, 295, 264, 1412, 8804, 420, 9134, 1951, 1045, 3832, 31219, 763, 295, 264, 914, 13, 407, 11803, 13, 22, 4, 295, 264, 1412, 9134, 1296, 2992, 3175], "avg_logprob": -0.21619317639957775, "compression_ratio": 1.5410958904109588, "no_speech_prob": 0.0, "words": [{"start": 490.59, "end": 491.13, "word": " And", "probability": 0.344482421875}, {"start": 491.13, "end": 495.41, "word": " finally,", "probability": 0.254150390625}, {"start": 495.79, "end": 497.73, "word": " approximately", "probability": 0.85986328125}, {"start": 497.73, "end": 498.23, "word": " 99", "probability": 0.92138671875}, {"start": 498.23, "end": 498.85, "word": ".7", "probability": 0.98486328125}, {"start": 498.85, "end": 499.25, "word": "%", "probability": 0.8203125}, {"start": 499.25, "end": 499.61, "word": " of", "probability": 0.958984375}, {"start": 499.61, "end": 499.73, "word": " the", "probability": 0.9208984375}, {"start": 499.73, "end": 499.97, "word": " data,", "probability": 0.94921875}, {"start": 500.11, "end": 500.21, "word": " it", "probability": 0.8564453125}, {"start": 500.21, "end": 500.57, "word": " means", "probability": 0.91357421875}, {"start": 500.57, "end": 501.27, "word": " almost", "probability": 0.76220703125}, {"start": 501.27, "end": 501.47, "word": " the", "probability": 0.65966796875}, {"start": 501.47, "end": 501.73, "word": " data.", "probability": 0.91748046875}, {"start": 502.15, "end": 502.49, "word": " Because", "probability": 0.80859375}, {"start": 502.49, "end": 502.61, "word": " we", "probability": 0.90087890625}, {"start": 502.61, "end": 502.73, "word": " are", "probability": 0.92041015625}, {"start": 502.73, "end": 503.11, "word": " saying", "probability": 0.791015625}, {"start": 503.11, "end": 503.99, "word": " 99", "probability": 0.87841796875}, {"start": 503.99, "end": 504.55, "word": ".7", "probability": 0.9951171875}, {"start": 504.55, "end": 504.91, "word": " means", "probability": 0.4228515625}, {"start": 504.91, "end": 505.35, "word": " most", "probability": 0.85595703125}, {"start": 505.35, "end": 505.49, "word": " of", "probability": 0.96826171875}, {"start": 505.49, "end": 505.61, "word": " the", "probability": 0.91845703125}, {"start": 505.61, "end": 505.97, "word": " data", "probability": 0.93408203125}, {"start": 505.97, "end": 507.51, "word": " falls", "probability": 0.68017578125}, {"start": 507.51, "end": 508.39, "word": " or", "probability": 0.85595703125}, {"start": 508.39, "end": 508.85, "word": " lies", "probability": 0.92626953125}, {"start": 508.85, "end": 509.21, "word": " within", "probability": 0.90087890625}, {"start": 509.21, "end": 509.55, "word": " three", "probability": 0.7060546875}, {"start": 509.55, "end": 509.93, "word": " standard", "probability": 0.90673828125}, {"start": 509.93, "end": 510.51, "word": " deviations", "probability": 0.929931640625}, {"start": 510.51, "end": 511.01, "word": " of", "probability": 0.9609375}, {"start": 511.01, "end": 511.17, "word": " the", "probability": 0.921875}, {"start": 511.17, "end": 511.37, "word": " mean.", "probability": 0.94775390625}, {"start": 512.85, "end": 513.23, "word": " So", "probability": 0.962890625}, {"start": 513.23, "end": 513.73, "word": " 99", "probability": 0.8408203125}, {"start": 513.73, "end": 515.35, "word": ".7", "probability": 0.99658203125}, {"start": 515.35, "end": 515.83, "word": "%", "probability": 0.98681640625}, {"start": 515.83, "end": 516.13, "word": " of", "probability": 0.958984375}, {"start": 516.13, "end": 516.27, "word": " the", "probability": 0.921875}, {"start": 516.27, "end": 516.63, "word": " data", "probability": 0.9453125}, {"start": 516.63, "end": 517.77, "word": " lies", "probability": 0.888671875}, {"start": 517.77, "end": 518.23, "word": " between", "probability": 0.888671875}, {"start": 518.23, "end": 518.51, "word": " mu", "probability": 0.70703125}, {"start": 518.51, "end": 518.99, "word": " minus", "probability": 0.966796875}], "temperature": 1.0}, {"id": 21, "seek": 54371, "start": 519.73, "end": 543.71, "text": " the pre-sigma and the mu plus of pre-sigma. 68, 95, 99.7 are fixed numbers. Later in chapter 6, we will explain in details other coefficients. Maybe suppose we are interested not in one of these. Suppose we are interested in 90% or 80% or 85%.", "tokens": [264, 659, 12, 82, 16150, 293, 264, 2992, 1804, 295, 659, 12, 82, 16150, 13, 23317, 11, 13420, 11, 11803, 13, 22, 366, 6806, 3547, 13, 11965, 294, 7187, 1386, 11, 321, 486, 2903, 294, 4365, 661, 31994, 13, 2704, 7297, 321, 366, 3102, 406, 294, 472, 295, 613, 13, 21360, 321, 366, 3102, 294, 4289, 4, 420, 4688, 4, 420, 14695, 6856], "avg_logprob": -0.24462891183793545, "compression_ratio": 1.4787878787878788, "no_speech_prob": 0.0, "words": [{"start": 519.73, "end": 519.97, "word": " the", "probability": 0.105712890625}, {"start": 519.97, "end": 520.17, "word": " pre", "probability": 0.2587890625}, {"start": 520.17, "end": 520.49, "word": "-sigma", "probability": 0.8709309895833334}, {"start": 520.49, "end": 520.85, "word": " and", "probability": 0.70654296875}, {"start": 520.85, "end": 520.99, "word": " the", "probability": 0.7373046875}, {"start": 520.99, "end": 521.05, "word": " mu", "probability": 0.6845703125}, {"start": 521.05, "end": 521.31, "word": " plus", "probability": 0.78759765625}, {"start": 521.31, "end": 521.47, "word": " of", "probability": 0.5224609375}, {"start": 521.47, "end": 521.67, "word": " pre", "probability": 0.383544921875}, {"start": 521.67, "end": 521.87, "word": "-sigma.", "probability": 0.9557291666666666}, {"start": 525.03, "end": 525.55, "word": " 68,", "probability": 0.8681640625}, {"start": 525.79, "end": 526.27, "word": " 95,", "probability": 0.95703125}, {"start": 526.47, "end": 526.69, "word": " 99", "probability": 0.95654296875}, {"start": 526.69, "end": 527.19, "word": ".7", "probability": 0.7978515625}, {"start": 527.19, "end": 527.55, "word": " are", "probability": 0.89111328125}, {"start": 527.55, "end": 527.87, "word": " fixed", "probability": 0.91650390625}, {"start": 527.87, "end": 528.31, "word": " numbers.", "probability": 0.89892578125}, {"start": 529.09, "end": 529.37, "word": " Later", "probability": 0.87890625}, {"start": 529.37, "end": 529.57, "word": " in", "probability": 0.79736328125}, {"start": 529.57, "end": 529.81, "word": " chapter", "probability": 0.53076171875}, {"start": 529.81, "end": 530.29, "word": " 6,", "probability": 0.51220703125}, {"start": 530.45, "end": 530.61, "word": " we", "probability": 0.94384765625}, {"start": 530.61, "end": 530.87, "word": " will", "probability": 0.85693359375}, {"start": 530.87, "end": 531.77, "word": " explain", "probability": 0.94921875}, {"start": 531.77, "end": 532.03, "word": " in", "probability": 0.8857421875}, {"start": 532.03, "end": 532.53, "word": " details", "probability": 0.81787109375}, {"start": 532.53, "end": 533.97, "word": " other", "probability": 0.76806640625}, {"start": 533.97, "end": 535.01, "word": " coefficients.", "probability": 0.9482421875}, {"start": 535.53, "end": 535.65, "word": " Maybe", "probability": 0.84033203125}, {"start": 535.65, "end": 536.13, "word": " suppose", "probability": 0.6337890625}, {"start": 536.13, "end": 536.33, "word": " we", "probability": 0.9296875}, {"start": 536.33, "end": 536.67, "word": " are", "probability": 0.9296875}, {"start": 536.67, "end": 537.07, "word": " interested", "probability": 0.7744140625}, {"start": 537.07, "end": 537.71, "word": " not", "probability": 0.63232421875}, {"start": 537.71, "end": 537.91, "word": " in", "probability": 0.93017578125}, {"start": 537.91, "end": 538.09, "word": " one", "probability": 0.92041015625}, {"start": 538.09, "end": 538.25, "word": " of", "probability": 0.9677734375}, {"start": 538.25, "end": 538.47, "word": " these.", "probability": 0.853515625}, {"start": 538.69, "end": 538.99, "word": " Suppose", "probability": 0.82373046875}, {"start": 538.99, "end": 540.27, "word": " we", "probability": 0.9287109375}, {"start": 540.27, "end": 540.49, "word": " are", "probability": 0.94140625}, {"start": 540.49, "end": 540.97, "word": " interested", "probability": 0.8369140625}, {"start": 540.97, "end": 541.21, "word": " in", "probability": 0.91796875}, {"start": 541.21, "end": 541.47, "word": " 90", "probability": 0.9833984375}, {"start": 541.47, "end": 541.71, "word": "%", "probability": 0.64111328125}, {"start": 541.71, "end": 542.07, "word": " or", "probability": 0.9482421875}, {"start": 542.07, "end": 542.37, "word": " 80", "probability": 0.9599609375}, {"start": 542.37, "end": 542.75, "word": "%", "probability": 0.97998046875}, {"start": 542.75, "end": 543.01, "word": " or", "probability": 0.96240234375}, {"start": 543.01, "end": 543.71, "word": " 85%.", "probability": 0.75244140625}], "temperature": 1.0}, {"id": 22, "seek": 56486, "start": 545.08, "end": 564.86, "text": " This rule just for 689599.7. This rule is called 689599.7 rule. That is, again, 68% of the data lies within one standard deviation of the mean.", "tokens": [639, 4978, 445, 337, 23317, 15718, 8494, 13, 22, 13, 639, 4978, 307, 1219, 23317, 15718, 8494, 13, 22, 4978, 13, 663, 307, 11, 797, 11, 23317, 4, 295, 264, 1412, 9134, 1951, 472, 3832, 25163, 295, 264, 914, 13], "avg_logprob": -0.1795922256097561, "compression_ratio": 1.3211009174311927, "no_speech_prob": 0.0, "words": [{"start": 545.08, "end": 545.5, "word": " This", "probability": 0.5888671875}, {"start": 545.5, "end": 545.74, "word": " rule", "probability": 0.8662109375}, {"start": 545.74, "end": 546.16, "word": " just", "probability": 0.4150390625}, {"start": 546.16, "end": 547.24, "word": " for", "probability": 0.91748046875}, {"start": 547.24, "end": 549.68, "word": " 689599", "probability": 0.8634440104166666}, {"start": 549.68, "end": 550.34, "word": ".7.", "probability": 0.77978515625}, {"start": 550.64, "end": 551.14, "word": " This", "probability": 0.859375}, {"start": 551.14, "end": 551.36, "word": " rule", "probability": 0.88916015625}, {"start": 551.36, "end": 551.5, "word": " is", "probability": 0.9453125}, {"start": 551.5, "end": 551.96, "word": " called", "probability": 0.87841796875}, {"start": 551.96, "end": 555.56, "word": " 689599", "probability": 0.9527994791666666}, {"start": 555.56, "end": 556.26, "word": ".7", "probability": 0.982177734375}, {"start": 556.26, "end": 556.94, "word": " rule.", "probability": 0.83984375}, {"start": 557.66, "end": 557.86, "word": " That", "probability": 0.880859375}, {"start": 557.86, "end": 558.2, "word": " is,", "probability": 0.94775390625}, {"start": 558.84, "end": 559.04, "word": " again,", "probability": 0.9501953125}, {"start": 560.08, "end": 560.5, "word": " 68", "probability": 0.9453125}, {"start": 560.5, "end": 560.84, "word": "%", "probability": 0.77001953125}, {"start": 560.84, "end": 561.14, "word": " of", "probability": 0.95166015625}, {"start": 561.14, "end": 561.28, "word": " the", "probability": 0.91552734375}, {"start": 561.28, "end": 561.6, "word": " data", "probability": 0.9541015625}, {"start": 561.6, "end": 562.96, "word": " lies", "probability": 0.880859375}, {"start": 562.96, "end": 563.32, "word": " within", "probability": 0.904296875}, {"start": 563.32, "end": 563.58, "word": " one", "probability": 0.91064453125}, {"start": 563.58, "end": 564.0, "word": " standard", "probability": 0.93701171875}, {"start": 564.0, "end": 564.38, "word": " deviation", "probability": 0.89990234375}, {"start": 564.38, "end": 564.6, "word": " of", "probability": 0.966796875}, {"start": 564.6, "end": 564.72, "word": " the", "probability": 0.9267578125}, {"start": 564.72, "end": 564.86, "word": " mean.", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 23, "seek": 59407, "start": 565.95, "end": 594.07, "text": " 95% of the data lies within two standard deviations of the mean. And finally, most of the data falls within three standard deviations of the mean. Let's see how can we use this empirical rule for a specific example. Imagine that the variable math set scores is bell shaped. So here we assume that", "tokens": [13420, 4, 295, 264, 1412, 9134, 1951, 732, 3832, 31219, 763, 295, 264, 914, 13, 400, 2721, 11, 881, 295, 264, 1412, 8804, 1951, 1045, 3832, 31219, 763, 295, 264, 914, 13, 961, 311, 536, 577, 393, 321, 764, 341, 31886, 4978, 337, 257, 2685, 1365, 13, 11739, 300, 264, 7006, 5221, 992, 13444, 307, 4549, 13475, 13, 407, 510, 321, 6552, 300], "avg_logprob": -0.17236328381113708, "compression_ratio": 1.6141304347826086, "no_speech_prob": 0.0, "words": [{"start": 565.95, "end": 566.37, "word": " 95", "probability": 0.7705078125}, {"start": 566.37, "end": 566.77, "word": "%", "probability": 0.80224609375}, {"start": 566.77, "end": 567.03, "word": " of", "probability": 0.9501953125}, {"start": 567.03, "end": 567.17, "word": " the", "probability": 0.9033203125}, {"start": 567.17, "end": 567.51, "word": " data", "probability": 0.94189453125}, {"start": 567.51, "end": 568.79, "word": " lies", "probability": 0.837890625}, {"start": 568.79, "end": 569.11, "word": 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"start": 595.23, "end": 620.59, "text": " The math status score has symmetric shape or bell shape. In this case, we can use the previous rule. Otherwise, we cannot. So assume the math status score is bell-shaped with a mean of 500. I mean, the population mean is 500 and standard deviation of 90.", "tokens": [440, 5221, 6558, 6175, 575, 32330, 3909, 420, 4549, 3909, 13, 682, 341, 1389, 11, 321, 393, 764, 264, 3894, 4978, 13, 10328, 11, 321, 2644, 13, 407, 6552, 264, 5221, 6558, 6175, 307, 4549, 12, 23103, 365, 257, 914, 295, 5923, 13, 286, 914, 11, 264, 4415, 914, 307, 5923, 293, 3832, 25163, 295, 4289, 13], "avg_logprob": -0.25121229270408896, "compression_ratio": 1.5548780487804879, "no_speech_prob": 0.0, "words": [{"start": 595.23, "end": 595.55, "word": " The", "probability": 0.42626953125}, {"start": 595.55, "end": 595.83, "word": " math", "probability": 0.63037109375}, {"start": 595.83, "end": 596.17, "word": " status", "probability": 0.283447265625}, {"start": 596.17, "end": 596.61, "word": " score", "probability": 0.66259765625}, {"start": 596.61, "end": 597.35, "word": " has", "probability": 0.869140625}, {"start": 597.35, "end": 599.11, "word": " symmetric", "probability": 0.51318359375}, {"start": 599.11, "end": 599.63, "word": " shape", "probability": 0.181884765625}, {"start": 599.63, "end": 600.55, "word": " or", "probability": 0.78076171875}, {"start": 600.55, "end": 600.95, "word": " bell", "probability": 0.86669921875}, {"start": 600.95, "end": 601.39, "word": " shape.", "probability": 0.740234375}, {"start": 601.81, "end": 602.33, "word": " In", "probability": 0.91650390625}, {"start": 602.33, "end": 602.59, "word": " this", "probability": 0.94970703125}, {"start": 602.59, "end": 602.87, "word": " case,", "probability": 0.91357421875}, {"start": 602.91, "end": 603.07, "word": " we", "probability": 0.9423828125}, {"start": 603.07, "end": 603.27, "word": " can", "probability": 0.9423828125}, {"start": 603.27, "end": 603.45, "word": " use", "probability": 0.86669921875}, {"start": 603.45, "end": 603.57, "word": " the", "probability": 0.8955078125}, {"start": 603.57, "end": 603.93, "word": " previous", "probability": 0.84765625}, {"start": 603.93, "end": 604.23, "word": " rule.", "probability": 0.91064453125}, {"start": 604.35, "end": 604.57, "word": " Otherwise,", "probability": 0.90771484375}, {"start": 604.77, "end": 604.89, "word": " we", "probability": 0.93505859375}, {"start": 604.89, "end": 605.17, "word": " cannot.", "probability": 0.85205078125}, {"start": 606.19, "end": 606.55, "word": " So", "probability": 0.8076171875}, {"start": 606.55, "end": 607.39, "word": " assume", "probability": 0.71533203125}, {"start": 607.39, "end": 608.79, "word": " the", "probability": 0.83935546875}, {"start": 608.79, "end": 609.33, "word": " math", "probability": 0.90966796875}, {"start": 609.33, "end": 609.61, "word": " status", "probability": 0.919921875}, {"start": 609.61, "end": 609.91, "word": " score", "probability": 0.7919921875}, {"start": 609.91, "end": 610.07, "word": " is", "probability": 0.89892578125}, {"start": 610.07, "end": 610.31, "word": " bell", "probability": 0.8994140625}, {"start": 610.31, "end": 610.67, "word": "-shaped", "probability": 0.700927734375}, {"start": 610.67, "end": 611.73, "word": " with", "probability": 0.77197265625}, {"start": 611.73, "end": 611.85, "word": " a", "probability": 0.955078125}, {"start": 611.85, "end": 611.99, "word": " mean", "probability": 0.978515625}, {"start": 611.99, "end": 612.15, "word": " of", "probability": 0.9677734375}, {"start": 612.15, "end": 612.67, "word": " 500.", "probability": 0.88720703125}, {"start": 614.85, "end": 615.55, "word": " I", "probability": 0.83740234375}, {"start": 615.55, "end": 615.75, "word": " mean,", "probability": 0.96142578125}, {"start": 616.41, "end": 616.65, "word": " the", "probability": 0.9052734375}, {"start": 616.65, "end": 617.01, "word": " population", "probability": 0.96484375}, {"start": 617.01, "end": 617.27, "word": " mean", "probability": 0.537109375}, {"start": 617.27, "end": 617.41, "word": " is", "probability": 0.9443359375}, {"start": 617.41, "end": 617.87, "word": " 500", "probability": 0.97265625}, {"start": 617.87, "end": 618.93, "word": " and", "probability": 0.64404296875}, {"start": 618.93, "end": 619.35, "word": " standard", "probability": 0.90576171875}, {"start": 619.35, "end": 619.75, "word": " deviation", "probability": 0.95166015625}, {"start": 619.75, "end": 620.15, "word": " of", "probability": 0.95166015625}, {"start": 620.15, "end": 620.59, "word": " 90.", "probability": 0.9765625}], "temperature": 1.0}, {"id": 25, "seek": 64848, "start": 621.66, "end": 648.48, "text": " And let's see how can we apply the empirical rule. So again, meta score has a mean of 500 and standard deviation sigma is 90. Then we can say that 60% of all test takers scored between 68%. So mu is 500.", "tokens": [400, 718, 311, 536, 577, 393, 321, 3079, 264, 31886, 4978, 13, 407, 797, 11, 19616, 6175, 575, 257, 914, 295, 5923, 293, 3832, 25163, 12771, 307, 4289, 13, 1396, 321, 393, 584, 300, 4060, 4, 295, 439, 1500, 991, 433, 18139, 1296, 23317, 6856, 407, 2992, 307, 5923, 13], "avg_logprob": -0.2005208356707704, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 621.66, "end": 621.98, "word": " And", "probability": 0.71630859375}, {"start": 621.98, "end": 622.32, "word": " let's", "probability": 0.94775390625}, {"start": 622.32, "end": 622.58, "word": " see", "probability": 0.86474609375}, {"start": 622.58, "end": 622.94, "word": " how", "probability": 0.77734375}, {"start": 622.94, "end": 623.24, "word": " can", "probability": 0.86376953125}, {"start": 623.24, "end": 623.38, "word": " we", "probability": 0.91259765625}, {"start": 623.38, "end": 623.88, "word": " apply", "probability": 0.9375}, {"start": 623.88, "end": 624.62, "word": " the", "probability": 0.875}, {"start": 624.62, "end": 625.12, "word": " empirical", "probability": 0.9208984375}, {"start": 625.12, "end": 625.46, "word": " rule.", "probability": 0.6728515625}, {"start": 626.12, "end": 626.3, "word": " So", "probability": 0.94873046875}, {"start": 626.3, "end": 626.62, "word": " again,", "probability": 0.7890625}, {"start": 627.48, "end": 627.7, "word": " meta", "probability": 0.1298828125}, {"start": 627.7, "end": 628.3, "word": " score", "probability": 0.6826171875}, {"start": 628.3, "end": 628.76, "word": " has", "probability": 0.9384765625}, {"start": 628.76, "end": 628.9, "word": " a", "probability": 0.97265625}, {"start": 628.9, "end": 629.02, "word": " mean", "probability": 0.9755859375}, {"start": 629.02, "end": 629.22, "word": " of", "probability": 0.97119140625}, {"start": 629.22, "end": 629.7, "word": " 500", "probability": 0.94384765625}, {"start": 629.7, "end": 631.12, "word": " and", "probability": 0.479248046875}, {"start": 631.12, "end": 631.86, "word": " standard", "probability": 0.93896484375}, {"start": 631.86, "end": 632.32, "word": " deviation", "probability": 0.9580078125}, {"start": 632.32, "end": 633.22, "word": " sigma", "probability": 0.60888671875}, {"start": 633.22, "end": 633.62, "word": " is", "probability": 0.94970703125}, {"start": 633.62, "end": 634.06, "word": " 90.", "probability": 0.9736328125}, {"start": 634.84, "end": 635.14, "word": " Then", "probability": 0.83544921875}, {"start": 635.14, "end": 635.3, "word": " we", "probability": 0.8798828125}, {"start": 635.3, "end": 635.5, "word": " can", "probability": 0.90576171875}, {"start": 635.5, "end": 635.72, "word": " say", "probability": 0.86767578125}, {"start": 635.72, "end": 635.96, "word": " that", "probability": 0.93310546875}, {"start": 635.96, "end": 637.66, "word": " 60", "probability": 0.8701171875}, {"start": 637.66, "end": 638.0, "word": "%", "probability": 0.845703125}, {"start": 638.0, "end": 638.5, "word": " of", "probability": 0.96923828125}, {"start": 638.5, "end": 638.9, "word": " all", "probability": 0.9326171875}, {"start": 638.9, "end": 639.34, "word": " test", "probability": 0.712890625}, {"start": 639.34, "end": 639.94, "word": " takers", "probability": 0.840576171875}, {"start": 639.94, "end": 641.28, "word": " scored", "probability": 0.89013671875}, {"start": 641.28, "end": 643.2, "word": " between", "probability": 0.859375}, {"start": 643.2, "end": 646.64, "word": " 68%.", "probability": 0.556884765625}, {"start": 646.64, "end": 647.16, "word": " So", "probability": 0.95556640625}, {"start": 647.16, "end": 647.54, "word": " mu", "probability": 0.63134765625}, {"start": 647.54, "end": 647.86, "word": " is", "probability": 0.9462890625}, {"start": 647.86, "end": 648.48, "word": " 500.", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 26, "seek": 67929, "start": 650.11, "end": 679.29, "text": " minus sigma is 90. And mu plus sigma, 500 plus 90. So you can say that 68% or 230 of all test takers scored between 410 and 590. So 68% of all test takers who took", "tokens": [3175, 12771, 307, 4289, 13, 400, 2992, 1804, 12771, 11, 5923, 1804, 4289, 13, 407, 291, 393, 584, 300, 23317, 4, 420, 35311, 295, 439, 1500, 991, 433, 18139, 1296, 1017, 3279, 293, 1025, 7771, 13, 407, 23317, 4, 295, 439, 1500, 991, 433, 567, 1890], "avg_logprob": -0.2202460119064818, "compression_ratio": 1.3442622950819672, "no_speech_prob": 0.0, "words": [{"start": 650.11, "end": 650.73, "word": " minus", "probability": 0.470703125}, {"start": 650.73, "end": 651.91, "word": " sigma", "probability": 0.7080078125}, {"start": 651.91, "end": 652.71, "word": " is", "probability": 0.8759765625}, {"start": 652.71, "end": 653.23, "word": " 90.", "probability": 0.8896484375}, {"start": 654.47, "end": 655.51, "word": " And", "probability": 0.341552734375}, {"start": 655.51, "end": 655.75, "word": " mu", "probability": 0.6689453125}, {"start": 655.75, "end": 656.55, "word": " plus", "probability": 0.94384765625}, {"start": 656.55, "end": 657.05, "word": " sigma,", "probability": 0.93310546875}, {"start": 657.81, "end": 658.37, "word": " 500", "probability": 0.96044921875}, {"start": 658.37, "end": 659.37, "word": " plus", "probability": 0.87451171875}, {"start": 659.37, "end": 659.85, "word": " 90.", "probability": 0.974609375}, {"start": 660.47, "end": 660.77, "word": " So", "probability": 0.9482421875}, {"start": 660.77, "end": 660.95, "word": " you", "probability": 0.84716796875}, {"start": 660.95, "end": 661.15, "word": " can", "probability": 0.9423828125}, {"start": 661.15, "end": 661.39, "word": " say", "probability": 0.71435546875}, {"start": 661.39, "end": 661.69, "word": " that", "probability": 0.8798828125}, {"start": 661.69, "end": 663.49, "word": " 68", "probability": 0.9287109375}, {"start": 663.49, "end": 663.93, "word": "%", "probability": 0.63916015625}, {"start": 663.93, "end": 664.71, "word": " or", "probability": 0.900390625}, {"start": 664.71, "end": 665.39, "word": " 230", "probability": 0.253662109375}, {"start": 665.39, "end": 667.17, "word": " of", "probability": 0.9033203125}, {"start": 667.17, "end": 667.63, "word": " all", "probability": 0.94287109375}, {"start": 667.63, "end": 667.89, "word": " test", "probability": 0.873046875}, {"start": 667.89, "end": 668.47, "word": " takers", "probability": 0.796875}, {"start": 668.47, "end": 669.31, "word": " scored", "probability": 0.8369140625}, {"start": 669.31, "end": 669.89, "word": " between", "probability": 0.87939453125}, {"start": 669.89, "end": 672.03, "word": " 410", "probability": 0.95166015625}, {"start": 672.03, "end": 673.01, "word": " and", "probability": 0.92919921875}, {"start": 673.01, "end": 674.39, "word": " 590.", "probability": 0.780029296875}, {"start": 674.91, "end": 675.61, "word": " So", "probability": 0.8876953125}, {"start": 675.61, "end": 675.99, "word": " 68", "probability": 0.97119140625}, {"start": 675.99, "end": 676.25, "word": "%", "probability": 0.9853515625}, {"start": 676.25, "end": 676.75, "word": " of", "probability": 0.96337890625}, {"start": 676.75, "end": 677.71, "word": " all", "probability": 0.7021484375}, {"start": 677.71, "end": 677.97, "word": " test", "probability": 0.7763671875}, {"start": 677.97, "end": 678.47, "word": " takers", "probability": 0.90869140625}, {"start": 678.47, "end": 678.93, "word": " who", "probability": 0.88720703125}, {"start": 678.93, "end": 679.29, "word": " took", "probability": 0.9208984375}], "temperature": 1.0}, {"id": 27, "seek": 70774, "start": 679.82, "end": 707.74, "text": " that exam scored between 14 and 590. That if we assume previously the data is well shaped, otherwise we cannot say that. For the other rule, 95% of all test takers scored between mu is 500 minus 2 times sigma, 500 plus 2 times sigma. So that means", "tokens": [300, 1139, 18139, 1296, 3499, 293, 1025, 7771, 13, 663, 498, 321, 6552, 8046, 264, 1412, 307, 731, 13475, 11, 5911, 321, 2644, 584, 300, 13, 1171, 264, 661, 4978, 11, 13420, 4, 295, 439, 1500, 991, 433, 18139, 1296, 2992, 307, 5923, 3175, 568, 1413, 12771, 11, 5923, 1804, 568, 1413, 12771, 13, 407, 300, 1355], "avg_logprob": -0.2147090527518042, "compression_ratio": 1.503030303030303, "no_speech_prob": 0.0, "words": [{"start": 679.82, "end": 680.24, "word": " that", "probability": 0.312255859375}, {"start": 680.24, "end": 681.66, "word": " exam", "probability": 0.9228515625}, {"start": 681.66, "end": 682.9, "word": " scored", "probability": 0.55224609375}, {"start": 682.9, "end": 683.38, "word": " between", "probability": 0.88330078125}, {"start": 683.38, "end": 684.16, "word": " 14", "probability": 0.865234375}, {"start": 684.16, "end": 684.68, "word": " and", "probability": 0.91357421875}, {"start": 684.68, "end": 685.8, "word": " 590.", "probability": 0.787841796875}, {"start": 685.98, "end": 686.44, "word": " That", "probability": 0.85546875}, {"start": 686.44, "end": 686.64, "word": " if", "probability": 0.791015625}, {"start": 686.64, "end": 686.8, "word": " we", "probability": 0.84130859375}, {"start": 686.8, "end": 687.26, "word": " assume", "probability": 0.86865234375}, {"start": 687.26, "end": 687.74, "word": " previously", "probability": 0.63232421875}, {"start": 687.74, "end": 688.02, "word": " the", "probability": 0.78955078125}, {"start": 688.02, "end": 688.3, "word": " data", "probability": 0.9306640625}, {"start": 688.3, "end": 688.5, "word": " is", "probability": 0.8720703125}, {"start": 688.5, "end": 688.66, "word": " well", "probability": 0.826171875}, {"start": 688.66, "end": 688.92, "word": " shaped,", "probability": 0.4921875}, {"start": 689.0, "end": 689.22, "word": " otherwise", "probability": 0.84326171875}, {"start": 689.22, "end": 689.52, "word": " we", "probability": 0.6298828125}, {"start": 689.52, "end": 689.72, "word": " cannot", "probability": 0.87451171875}, {"start": 689.72, "end": 689.98, "word": " say", "probability": 0.60595703125}, {"start": 689.98, "end": 690.16, "word": " that.", "probability": 0.93505859375}, {"start": 691.18, "end": 691.56, "word": " For", "probability": 0.9443359375}, {"start": 691.56, "end": 691.7, "word": " the", "probability": 0.9228515625}, {"start": 691.7, "end": 691.94, "word": " other", "probability": 0.90185546875}, {"start": 691.94, "end": 692.28, "word": " rule,", "probability": 0.6513671875}, {"start": 692.74, "end": 693.14, "word": " 95", "probability": 0.97021484375}, {"start": 693.14, "end": 693.84, "word": "%", "probability": 0.77490234375}, {"start": 693.84, "end": 695.1, "word": " of", "probability": 0.96728515625}, {"start": 695.1, "end": 695.52, "word": " all", "probability": 0.94580078125}, {"start": 695.52, "end": 695.9, "word": " test", "probability": 0.8740234375}, {"start": 695.9, "end": 696.42, "word": " takers", "probability": 0.8095703125}, {"start": 696.42, "end": 696.84, "word": " scored", "probability": 0.89306640625}, {"start": 696.84, "end": 697.32, "word": " between", "probability": 0.88330078125}, {"start": 697.32, "end": 698.56, "word": " mu", "probability": 0.6259765625}, {"start": 698.56, "end": 698.84, "word": " is", "probability": 0.8818359375}, {"start": 698.84, "end": 699.4, "word": " 500", "probability": 0.96337890625}, {"start": 699.4, "end": 701.2, "word": " minus", "probability": 0.9072265625}, {"start": 701.2, "end": 701.5, "word": " 2", "probability": 0.736328125}, {"start": 701.5, "end": 701.8, "word": " times", "probability": 0.94091796875}, {"start": 701.8, "end": 702.18, "word": " sigma,", "probability": 0.9228515625}, {"start": 703.54, "end": 704.4, "word": " 500", "probability": 0.96435546875}, {"start": 704.4, "end": 704.92, "word": " plus", "probability": 0.95166015625}, {"start": 704.92, "end": 705.14, "word": " 2", "probability": 0.97314453125}, {"start": 705.14, "end": 705.42, "word": " times", "probability": 0.9365234375}, {"start": 705.42, "end": 705.78, "word": " sigma.", "probability": 0.93603515625}, {"start": 706.52, "end": 707.12, "word": " So", "probability": 0.953125}, {"start": 707.12, "end": 707.36, "word": " that", "probability": 0.830078125}, {"start": 707.36, "end": 707.74, "word": " means", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 28, "seek": 72786, "start": 708.16, "end": 727.86, "text": " 500 minus 180 is 320. 500 plus 180 is 680. So you can say that approximately 95% of all test takers scored between 320 and 680. Finally, you can say that", "tokens": [5923, 3175, 11971, 307, 42429, 13, 5923, 1804, 11971, 307, 1386, 4702, 13, 407, 291, 393, 584, 300, 10447, 13420, 4, 295, 439, 1500, 991, 433, 18139, 1296, 42429, 293, 1386, 4702, 13, 6288, 11, 291, 393, 584, 300], "avg_logprob": -0.1736328162252903, "compression_ratio": 1.2833333333333334, "no_speech_prob": 0.0, "words": [{"start": 708.16, "end": 708.68, "word": " 500", "probability": 0.8740234375}, {"start": 708.68, "end": 709.1, "word": " minus", "probability": 0.88916015625}, {"start": 709.1, "end": 709.54, "word": " 180", "probability": 0.3466796875}, {"start": 709.54, "end": 709.76, "word": " is", "probability": 0.9111328125}, {"start": 709.76, "end": 710.16, "word": " 320.", "probability": 0.9091796875}, {"start": 711.42, "end": 712.28, "word": " 500", "probability": 0.935546875}, {"start": 712.28, "end": 712.72, "word": " plus", "probability": 0.9462890625}, {"start": 712.72, "end": 713.1, "word": " 180", "probability": 0.91015625}, 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"text": " all of the test takers, approximately all, because when we are saying 99.7 it means just 0.3 is the rest, so you can say approximately all test takers scored between mu minus three sigma which is 90 and mu", "tokens": [439, 295, 264, 1500, 991, 433, 11, 10447, 439, 11, 570, 562, 321, 366, 1566, 11803, 13, 22, 309, 1355, 445, 1958, 13, 18, 307, 264, 1472, 11, 370, 291, 393, 584, 10447, 439, 1500, 991, 433, 18139, 1296, 2992, 3175, 1045, 12771, 597, 307, 4289, 293, 2992], "avg_logprob": -0.28523595965638454, "compression_ratio": 1.4609929078014185, "no_speech_prob": 0.0, "words": [{"start": 730.77, "end": 731.23, "word": " all", "probability": 0.393310546875}, {"start": 731.23, "end": 731.53, "word": " of", "probability": 0.95458984375}, {"start": 731.53, "end": 731.71, "word": " the", "probability": 0.92431640625}, {"start": 731.71, "end": 731.95, "word": " test", "probability": 0.87353515625}, {"start": 731.95, "end": 732.35, "word": " takers,", "probability": 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" It lost 3 seconds. So 500 minus 3 times 9 is 270. So that's 230. 500 plus 270 is 770. So we can say that 99.7% of all the stackers scored between 230 and 770. I will give another example just to make sure that you understand the meaning of this rule.", "tokens": [467, 2731, 805, 3949, 13, 407, 5923, 3175, 805, 1413, 1722, 307, 40774, 13, 407, 300, 311, 35311, 13, 5923, 1804, 40774, 307, 1614, 5867, 13, 407, 321, 393, 584, 300, 11803, 13, 22, 4, 295, 439, 264, 8630, 433, 18139, 1296, 35311, 293, 1614, 5867, 13, 286, 486, 976, 1071, 1365, 445, 281, 652, 988, 300, 291, 1223, 264, 3620, 295, 341, 4978, 13], "avg_logprob": -0.22194601821176935, "compression_ratio": 1.4342857142857144, "no_speech_prob": 0.0, "words": [{"start": 753.43, "end": 753.71, "word": " It", "probability": 0.1190185546875}, {"start": 753.71, "end": 754.01, "word": " lost", "probability": 0.52783203125}, {"start": 754.01, "end": 754.39, "word": " 3", "probability": 0.281982421875}, {"start": 754.39, "end": 754.65, "word": " seconds.", "probability": 0.271484375}, {"start": 756.47, "end": 756.67, "word": " So", "probability": 0.9365234375}, {"start": 756.67, "end": 757.13, "word": " 500", "probability": 0.89404296875}, {"start": 757.13, "end": 757.73, "word": " minus", "probability": 0.986328125}, {"start": 757.73, "end": 758.83, "word": " 3", "probability": 0.7802734375}, {"start": 758.83, "end": 759.35, "word": " times", "probability": 0.93896484375}, {"start": 759.35, "end": 759.83, "word": " 9", "probability": 0.904296875}, {"start": 759.83, "end": 760.05, "word": " is", "probability": 0.779296875}, {"start": 760.05, "end": 760.55, "word": " 270.", "probability": 0.9716796875}, {"start": 760.77, "end": 760.97, "word": " So", "probability": 0.9482421875}, {"start": 760.97, "end": 761.31, "word": " that's", "probability": 0.95947265625}, {"start": 761.31, "end": 761.75, "word": " 230.", "probability": 0.951171875}, {"start": 762.69, "end": 763.41, "word": " 500", "probability": 0.9482421875}, {"start": 763.41, "end": 763.67, "word": " plus", "probability": 0.79248046875}, {"start": 763.67, "end": 764.07, "word": " 270", "probability": 0.958984375}, {"start": 764.07, "end": 764.37, "word": " is", "probability": 0.935546875}, {"start": 764.37, "end": 765.03, "word": " 770.", "probability": 0.88427734375}, {"start": 765.57, "end": 765.81, "word": " So", "probability": 0.955078125}, {"start": 765.81, "end": 765.95, "word": " we", "probability": 0.4306640625}, {"start": 765.95, "end": 766.07, "word": " can", "probability": 0.9423828125}, {"start": 766.07, "end": 766.25, "word": " say", "probability": 0.69873046875}, {"start": 766.25, "end": 766.45, "word": " that", "probability": 0.923828125}, {"start": 766.45, "end": 766.77, "word": " 99", "probability": 0.412841796875}, {"start": 766.77, "end": 767.27, "word": ".7", "probability": 0.989013671875}, {"start": 767.27, "end": 767.65, "word": "%", "probability": 0.96533203125}, {"start": 767.65, "end": 767.99, "word": " of", "probability": 0.9609375}, {"start": 767.99, "end": 768.71, "word": " all", "probability": 0.94140625}, {"start": 768.71, "end": 768.93, "word": " the", "probability": 0.69873046875}, {"start": 768.93, "end": 769.47, "word": " stackers", "probability": 0.587890625}, {"start": 769.47, "end": 769.69, "word": " scored", "probability": 0.796875}, {"start": 769.69, "end": 770.19, "word": " between", "probability": 0.861328125}, {"start": 770.19, "end": 771.65, "word": " 230", "probability": 0.9501953125}, {"start": 771.65, "end": 772.13, "word": " and", "probability": 0.93798828125}, {"start": 772.13, "end": 772.97, "word": " 770.", "probability": 0.9599609375}, {"start": 774.27, "end": 774.49, "word": " I", "probability": 0.9990234375}, {"start": 774.49, "end": 774.61, "word": " will", "probability": 0.8310546875}, {"start": 774.61, "end": 774.81, "word": " give", "probability": 0.876953125}, {"start": 774.81, "end": 775.15, "word": " another", "probability": 0.91943359375}, {"start": 775.15, "end": 775.61, "word": " example", "probability": 0.97412109375}, {"start": 775.61, "end": 776.31, "word": " just", "probability": 0.61083984375}, {"start": 776.31, "end": 776.45, "word": " to", "probability": 0.96923828125}, {"start": 776.45, "end": 776.59, "word": " make", "probability": 0.9306640625}, {"start": 776.59, "end": 776.75, "word": " sure", "probability": 0.912109375}, {"start": 776.75, "end": 776.93, "word": " that", "probability": 0.931640625}, {"start": 776.93, "end": 777.03, "word": " you", "probability": 0.9365234375}, {"start": 777.03, "end": 777.69, "word": " understand", "probability": 0.8046875}, {"start": 777.69, "end": 778.93, "word": " the", "probability": 0.9189453125}, {"start": 778.93, "end": 779.21, "word": " meaning", "probability": 0.87646484375}, {"start": 779.21, "end": 780.19, "word": " of", "probability": 0.96533203125}, {"start": 780.19, "end": 780.49, "word": " this", "probability": 0.94482421875}, {"start": 780.49, "end": 780.87, "word": " rule.", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 31, "seek": 81154, "start": 783.62, "end": 811.54, "text": " For business, a statistic goes. For business, a statistic example. Suppose the scores are bell-shaped. So we are assuming the data is bell-shaped.", "tokens": [1171, 1606, 11, 257, 29588, 1709, 13, 1171, 1606, 11, 257, 29588, 1365, 13, 21360, 264, 13444, 366, 4549, 12, 23103, 13, 407, 321, 366, 11926, 264, 1412, 307, 4549, 12, 23103, 13], "avg_logprob": -0.331112141994869, "compression_ratio": 1.4848484848484849, "no_speech_prob": 0.0, "words": [{"start": 783.62, "end": 784.62, "word": " For", "probability": 0.564453125}, {"start": 784.62, "end": 785.2, "word": " business,", "probability": 0.87939453125}, {"start": 786.5, "end": 788.82, "word": " a", "probability": 0.1746826171875}, {"start": 788.82, "end": 789.22, "word": " statistic", "probability": 0.54833984375}, {"start": 789.22, "end": 789.72, "word": " goes.", "probability": 0.7255859375}, {"start": 795.72, "end": 796.34, "word": " For", "probability": 0.89990234375}, {"start": 796.34, "end": 796.68, "word": " business,", "probability": 0.9169921875}, {"start": 796.82, "end": 796.92, "word": " a", "probability": 0.61865234375}, {"start": 796.92, "end": 797.18, "word": " statistic", "probability": 0.8134765625}, {"start": 797.18, "end": 797.66, "word": " example.", "probability": 0.37255859375}, {"start": 799.74, "end": 800.26, "word": " Suppose", "probability": 0.8037109375}, {"start": 800.26, "end": 800.72, "word": " the", "probability": 0.89892578125}, {"start": 800.72, "end": 802.84, "word": " scores", "probability": 0.62451171875}, {"start": 802.84, "end": 803.78, "word": " are", "probability": 0.93603515625}, {"start": 803.78, "end": 804.12, "word": " bell", "probability": 0.60546875}, {"start": 804.12, "end": 804.48, "word": "-shaped.", "probability": 0.659912109375}, {"start": 805.02, "end": 805.56, "word": " So", "probability": 0.59521484375}, {"start": 805.56, "end": 805.74, "word": " we", "probability": 0.8466796875}, {"start": 805.74, "end": 805.92, "word": " are", "probability": 0.444091796875}, {"start": 805.92, "end": 807.44, "word": " assuming", "probability": 0.89306640625}, {"start": 807.44, "end": 809.74, "word": " the", "probability": 0.89453125}, {"start": 809.74, "end": 810.16, "word": " data", "probability": 0.9580078125}, {"start": 810.16, "end": 811.04, "word": " is", "probability": 0.9189453125}, {"start": 811.04, "end": 811.28, "word": " bell", "probability": 0.91162109375}, {"start": 811.28, "end": 811.54, "word": "-shaped.", "probability": 0.846923828125}], "temperature": 1.0}, {"id": 32, "seek": 83843, "start": 813.73, "end": 838.43, "text": " with mean of 75 and standard deviation of 5. Also, let's assume that 100 students took the exam. So we have 100 students.", "tokens": [365, 914, 295, 9562, 293, 3832, 25163, 295, 1025, 13, 2743, 11, 718, 311, 6552, 300, 2319, 1731, 1890, 264, 1139, 13, 407, 321, 362, 2319, 1731, 13], "avg_logprob": -0.129445049269446, "compression_ratio": 1.1844660194174756, "no_speech_prob": 0.0, "words": [{"start": 813.73, "end": 814.11, "word": " with", "probability": 0.47216796875}, {"start": 814.11, "end": 814.39, "word": " mean", "probability": 0.92333984375}, {"start": 814.39, "end": 814.91, "word": " of", "probability": 0.9521484375}, {"start": 814.91, "end": 817.55, "word": " 75", "probability": 0.78955078125}, {"start": 817.55, "end": 819.67, "word": " and", "probability": 0.75390625}, {"start": 819.67, "end": 820.97, "word": " standard", "probability": 0.89990234375}, {"start": 820.97, "end": 821.37, "word": " deviation", "probability": 0.95263671875}, {"start": 821.37, "end": 821.63, "word": " of", "probability": 0.96875}, {"start": 821.63, "end": 821.95, "word": " 5.", "probability": 0.74267578125}, {"start": 824.99, "end": 825.81, "word": " Also,", "probability": 0.94287109375}, {"start": 826.11, "end": 826.39, "word": " let's", "probability": 0.964599609375}, {"start": 826.39, "end": 826.71, "word": " assume", "probability": 0.9140625}, {"start": 826.71, "end": 827.19, "word": " that", "probability": 0.931640625}, {"start": 827.19, "end": 828.09, "word": " 100", "probability": 0.88623046875}, {"start": 828.09, "end": 828.95, "word": " students", "probability": 0.970703125}, {"start": 828.95, "end": 833.81, "word": " took", "probability": 0.87744140625}, {"start": 833.81, "end": 834.01, "word": " the", "probability": 0.919921875}, {"start": 834.01, "end": 834.27, "word": " exam.", "probability": 0.97021484375}, {"start": 835.71, "end": 836.67, "word": " So", "probability": 0.95751953125}, {"start": 836.67, "end": 837.07, "word": " we", "probability": 0.677734375}, {"start": 837.07, "end": 837.37, "word": " have", "probability": 0.94677734375}, {"start": 837.37, "end": 837.85, "word": " 100", "probability": 0.9326171875}, {"start": 837.85, "end": 838.43, "word": " students.", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 33, "seek": 86558, "start": 839.72, "end": 865.58, "text": " Last year took the exam of business statistics. The mean was 75. And standard deviation was 5. And let's see how it can tell about 6 to 8% rule. It means that 6 to 8% of all the students score between mu minus sigma. Mu is 75.", "tokens": [5264, 1064, 1890, 264, 1139, 295, 1606, 12523, 13, 440, 914, 390, 9562, 13, 400, 3832, 25163, 390, 1025, 13, 400, 718, 311, 536, 577, 309, 393, 980, 466, 1386, 281, 1649, 4, 4978, 13, 467, 1355, 300, 1386, 281, 1649, 4, 295, 439, 264, 1731, 6175, 1296, 2992, 3175, 12771, 13, 15601, 307, 9562, 13], "avg_logprob": -0.23177083124194228, "compression_ratio": 1.41875, "no_speech_prob": 0.0, "words": [{"start": 839.72, "end": 840.08, "word": " Last", "probability": 0.6611328125}, {"start": 840.08, "end": 840.38, "word": " year", "probability": 0.93505859375}, {"start": 840.38, "end": 840.84, "word": " took", "probability": 0.39013671875}, {"start": 840.84, "end": 841.04, "word": " the", "probability": 0.90673828125}, {"start": 841.04, "end": 841.42, "word": " exam", "probability": 0.96875}, {"start": 841.42, "end": 841.8, "word": " of", "probability": 0.94384765625}, {"start": 841.8, "end": 842.24, "word": " business", "probability": 0.7861328125}, {"start": 842.24, "end": 843.0, "word": " statistics.", "probability": 0.9072265625}, {"start": 844.18, "end": 844.36, "word": " The", "probability": 0.8583984375}, {"start": 844.36, "end": 844.5, "word": " mean", "probability": 0.96826171875}, {"start": 844.5, "end": 844.82, "word": " was", "probability": 0.953125}, {"start": 844.82, "end": 845.36, "word": " 75.", "probability": 0.91357421875}, {"start": 846.24, "end": 846.34, "word": " And", "probability": 0.393310546875}, {"start": 846.34, "end": 847.24, "word": " standard", "probability": 0.548828125}, {"start": 847.24, "end": 847.58, "word": " deviation", "probability": 0.818359375}, {"start": 847.58, "end": 847.96, "word": " was", "probability": 0.94970703125}, {"start": 847.96, "end": 848.5, "word": " 5.", "probability": 0.67529296875}, {"start": 849.48, "end": 849.8, "word": " And", "probability": 0.9150390625}, {"start": 849.8, "end": 850.08, "word": " let's", "probability": 0.86474609375}, {"start": 850.08, "end": 850.38, "word": " see", "probability": 0.69140625}, {"start": 850.38, "end": 850.78, "word": " how", "probability": 0.8408203125}, {"start": 850.78, "end": 850.92, "word": " it", "probability": 0.416748046875}, {"start": 850.92, "end": 851.12, "word": " can", "probability": 0.92822265625}, {"start": 851.12, "end": 851.4, "word": " tell", "probability": 0.8037109375}, {"start": 851.4, "end": 851.72, "word": " about", "probability": 0.90869140625}, {"start": 851.72, "end": 852.02, "word": " 6", "probability": 0.701171875}, {"start": 852.02, "end": 852.14, "word": " to", "probability": 0.4375}, {"start": 852.14, "end": 852.3, "word": " 8", "probability": 0.9970703125}, {"start": 852.3, "end": 852.68, "word": "%", "probability": 0.64208984375}, {"start": 852.68, "end": 853.98, "word": " rule.", "probability": 0.708984375}, {"start": 854.56, "end": 854.9, "word": " It", "probability": 0.95947265625}, {"start": 854.9, "end": 855.3, "word": " means", "probability": 0.931640625}, {"start": 855.3, "end": 855.68, "word": " that", "probability": 0.93408203125}, {"start": 855.68, "end": 856.6, "word": " 6", "probability": 0.93798828125}, {"start": 856.6, "end": 856.68, "word": " to", "probability": 0.892578125}, {"start": 856.68, "end": 856.84, "word": " 8", "probability": 0.9990234375}, {"start": 856.84, "end": 857.1, "word": "%", "probability": 0.99072265625}, {"start": 857.1, "end": 857.82, "word": " of", "probability": 0.95849609375}, {"start": 857.82, "end": 858.12, "word": " all", "probability": 0.9501953125}, {"start": 858.12, "end": 858.3, "word": " the", "probability": 0.87255859375}, {"start": 858.3, "end": 858.86, "word": " students", "probability": 0.97265625}, {"start": 858.86, "end": 862.1, "word": " score", "probability": 0.49267578125}, {"start": 862.1, "end": 862.62, "word": " between", "probability": 0.86083984375}, {"start": 862.62, "end": 863.92, "word": " mu", "probability": 0.424560546875}, {"start": 863.92, "end": 864.28, "word": " minus", "probability": 0.984375}, {"start": 864.28, "end": 864.7, "word": " sigma.", "probability": 0.93994140625}, {"start": 864.88, "end": 865.02, "word": " Mu", "probability": 0.91455078125}, {"start": 865.02, "end": 865.2, "word": " is", "probability": 0.92919921875}, {"start": 865.2, "end": 865.58, "word": " 75.", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 34, "seek": 89359, "start": 866.85, "end": 893.59, "text": " minus sigma and the mu plus sigma. So that means 68 students, because we have 100, so you can say 68 students scored between 70 and 80. So 60 students out of 100 scored between 70 and 80.", "tokens": [3175, 12771, 293, 264, 2992, 1804, 12771, 13, 407, 300, 1355, 23317, 1731, 11, 570, 321, 362, 2319, 11, 370, 291, 393, 584, 23317, 1731, 18139, 1296, 5285, 293, 4688, 13, 407, 4060, 1731, 484, 295, 2319, 18139, 1296, 5285, 293, 4688, 13], "avg_logprob": -0.2563920366493138, "compression_ratio": 1.5666666666666667, "no_speech_prob": 0.0, "words": [{"start": 866.85, "end": 867.29, "word": " minus", "probability": 0.6240234375}, {"start": 867.29, "end": 867.71, "word": " sigma", "probability": 0.72998046875}, {"start": 867.71, "end": 868.65, "word": " and", "probability": 0.740234375}, {"start": 868.65, "end": 868.81, "word": " the", "probability": 0.316162109375}, {"start": 868.81, "end": 868.99, "word": " mu", "probability": 0.60400390625}, {"start": 868.99, "end": 869.31, "word": " plus", "probability": 0.95166015625}, {"start": 869.31, "end": 869.61, "word": " sigma.", "probability": 0.91162109375}, {"start": 873.59, "end": 874.47, "word": " So", "probability": 0.87353515625}, {"start": 874.47, "end": 874.71, "word": " that", "probability": 0.8173828125}, {"start": 874.71, "end": 875.05, "word": " means", "probability": 0.9306640625}, {"start": 875.05, "end": 875.79, "word": " 68", "probability": 0.8603515625}, {"start": 875.79, "end": 876.85, "word": " students,", "probability": 0.974609375}, {"start": 877.15, "end": 877.47, "word": " because", "probability": 0.890625}, {"start": 877.47, "end": 877.61, "word": " we", "probability": 0.90673828125}, {"start": 877.61, "end": 877.75, "word": " have", "probability": 0.91357421875}, {"start": 877.75, "end": 878.01, "word": " 100,", "probability": 0.1400146484375}, {"start": 879.01, "end": 879.29, "word": " so", "probability": 0.61328125}, {"start": 879.29, "end": 879.41, "word": " you", "probability": 0.90283203125}, {"start": 879.41, "end": 879.57, "word": " can", "probability": 0.93505859375}, {"start": 879.57, "end": 879.77, "word": " say", "probability": 0.60888671875}, {"start": 879.77, "end": 880.29, "word": " 68", "probability": 0.96044921875}, {"start": 880.29, "end": 880.89, "word": " students", "probability": 0.97998046875}, {"start": 880.89, "end": 881.93, "word": " scored", "probability": 0.71435546875}, {"start": 881.93, "end": 882.37, "word": " between", "probability": 0.8720703125}, {"start": 882.37, "end": 883.15, "word": " 70", "probability": 0.6943359375}, {"start": 883.15, "end": 883.67, "word": " and", "probability": 0.904296875}, {"start": 883.67, "end": 885.41, "word": " 80.", "probability": 0.8740234375}, {"start": 886.61, "end": 887.49, "word": " So", "probability": 0.916015625}, {"start": 887.49, "end": 887.81, "word": " 60", "probability": 0.82080078125}, {"start": 887.81, "end": 888.33, "word": " students", "probability": 0.970703125}, {"start": 888.33, "end": 888.67, "word": " out", "probability": 0.8837890625}, {"start": 888.67, "end": 888.83, "word": " of", "probability": 0.974609375}, {"start": 888.83, "end": 889.29, "word": " 100", "probability": 0.927734375}, {"start": 889.29, "end": 890.65, "word": " scored", "probability": 0.81640625}, {"start": 890.65, "end": 891.17, "word": " between", "probability": 0.8720703125}, {"start": 891.17, "end": 892.61, "word": " 70", "probability": 0.98681640625}, {"start": 892.61, "end": 893.29, "word": " and", "probability": 0.94287109375}, {"start": 893.29, "end": 893.59, "word": " 80.", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 35, "seek": 91377, "start": 894.95, "end": 913.77, "text": " About 95 students out of 100 scored between 75 minus 2 times 5. 75 plus 2 times 5. So that gives 65.", "tokens": [7769, 13420, 1731, 484, 295, 2319, 18139, 1296, 9562, 3175, 568, 1413, 1025, 13, 9562, 1804, 568, 1413, 1025, 13, 407, 300, 2709, 11624, 13], "avg_logprob": -0.2546574633855086, "compression_ratio": 1.1744186046511629, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 894.95, "end": 895.25, "word": " About", "probability": 0.48095703125}, {"start": 895.25, "end": 897.19, "word": " 95", "probability": 0.88623046875}, {"start": 897.19, "end": 897.89, "word": " students", "probability": 0.90087890625}, {"start": 897.89, "end": 898.21, "word": " out", "probability": 0.8623046875}, {"start": 898.21, "end": 898.39, "word": " of", "probability": 0.97412109375}, {"start": 898.39, "end": 899.09, "word": " 100", "probability": 0.89111328125}, {"start": 899.09, "end": 900.77, "word": " scored", "probability": 0.62451171875}, {"start": 900.77, "end": 901.23, "word": " between", "probability": 0.90087890625}, {"start": 901.23, "end": 902.99, "word": " 75", "probability": 0.6630859375}, {"start": 902.99, "end": 903.57, "word": " minus", "probability": 0.92919921875}, {"start": 903.57, "end": 903.89, "word": " 2", "probability": 0.70849609375}, {"start": 903.89, "end": 904.17, "word": " times", "probability": 0.8994140625}, {"start": 904.17, "end": 904.53, "word": " 5.", "probability": 0.95361328125}, {"start": 905.55, "end": 906.71, "word": " 75", "probability": 0.78515625}, {"start": 906.71, "end": 907.27, "word": " plus", "probability": 0.9345703125}, {"start": 907.27, "end": 907.55, "word": " 2", "probability": 0.96923828125}, {"start": 907.55, "end": 908.29, "word": " times", "probability": 0.8154296875}, {"start": 908.29, "end": 908.73, "word": " 5.", "probability": 0.95947265625}, {"start": 909.85, "end": 910.73, "word": " So", "probability": 0.908203125}, {"start": 910.73, "end": 911.01, "word": " that", "probability": 0.8486328125}, {"start": 911.01, "end": 912.19, "word": " gives", "probability": 0.62890625}, {"start": 912.19, "end": 913.77, "word": " 65.", "probability": 0.951171875}], "temperature": 1.0}, {"id": 36, "seek": 94461, "start": 915.55, "end": 944.61, "text": " The minimum and the maximum is 85. So you can say that around 95 students scored between 65 and 85. Finally, maybe you can see all students. Because when you're saying 99.7, it means almost all the students scored between 75 minus 3 times Y.", "tokens": [440, 7285, 293, 264, 6674, 307, 14695, 13, 407, 291, 393, 584, 300, 926, 13420, 1731, 18139, 1296, 11624, 293, 14695, 13, 6288, 11, 1310, 291, 393, 536, 439, 1731, 13, 1436, 562, 291, 434, 1566, 11803, 13, 22, 11, 309, 1355, 1920, 439, 264, 1731, 18139, 1296, 9562, 3175, 805, 1413, 398, 13], "avg_logprob": -0.2305397711016915, "compression_ratio": 1.5031055900621118, "no_speech_prob": 0.0, "words": [{"start": 915.55, "end": 916.19, "word": " The", "probability": 0.4423828125}, {"start": 916.19, "end": 916.47, "word": " minimum", "probability": 0.91845703125}, {"start": 916.47, "end": 917.17, "word": " and", "probability": 0.80908203125}, {"start": 917.17, "end": 917.33, "word": " the", "probability": 0.83203125}, {"start": 917.33, "end": 917.71, "word": " maximum", "probability": 0.9111328125}, {"start": 917.71, "end": 918.09, "word": " is", "probability": 0.8212890625}, {"start": 918.09, "end": 918.41, "word": " 85.", "probability": 0.9169921875}, {"start": 919.41, "end": 920.19, "word": " So", "probability": 0.9052734375}, {"start": 920.19, "end": 920.53, "word": " you", "probability": 0.77880859375}, {"start": 920.53, "end": 920.77, "word": " can", "probability": 0.93310546875}, {"start": 920.77, "end": 920.95, "word": " say", "probability": 0.63427734375}, {"start": 920.95, "end": 921.29, "word": " that", "probability": 0.91943359375}, {"start": 921.29, "end": 921.73, "word": " around", "probability": 0.79443359375}, {"start": 921.73, "end": 922.29, "word": " 95", "probability": 0.9638671875}, {"start": 922.29, "end": 923.71, "word": " students", "probability": 0.48095703125}, {"start": 923.71, "end": 924.61, "word": " scored", "probability": 0.87158203125}, {"start": 924.61, "end": 924.95, "word": " between", "probability": 0.82861328125}, {"start": 924.95, "end": 925.39, "word": " 65", "probability": 0.97998046875}, {"start": 925.39, "end": 925.65, "word": " and", "probability": 0.93310546875}, {"start": 925.65, "end": 925.93, "word": " 85.", "probability": 0.78076171875}, {"start": 926.65, "end": 927.43, "word": " Finally,", "probability": 0.642578125}, {"start": 928.13, "end": 929.23, "word": " maybe", "probability": 0.87841796875}, {"start": 929.23, "end": 929.81, "word": " you", "probability": 0.90283203125}, {"start": 929.81, "end": 930.01, "word": " can", "probability": 0.94482421875}, {"start": 930.01, "end": 930.21, "word": " see", "probability": 0.7568359375}, {"start": 930.21, "end": 930.61, "word": " all", "probability": 0.84814453125}, {"start": 930.61, "end": 931.93, "word": " students.", "probability": 0.833984375}, {"start": 933.11, "end": 933.51, "word": " Because", "probability": 0.92626953125}, {"start": 933.51, "end": 933.69, "word": " when", "probability": 0.8291015625}, {"start": 933.69, "end": 933.99, "word": " you're", "probability": 0.7080078125}, {"start": 933.99, "end": 934.35, "word": " saying", "probability": 0.8876953125}, {"start": 934.35, "end": 934.65, "word": " 99", "probability": 0.274169921875}, {"start": 934.65, "end": 935.25, "word": ".7,", "probability": 0.772216796875}, {"start": 936.47, "end": 936.73, "word": " it", "probability": 0.828125}, {"start": 936.73, "end": 937.09, "word": " means", "probability": 0.91357421875}, {"start": 937.09, "end": 938.19, "word": " almost", "probability": 0.78076171875}, {"start": 938.19, "end": 938.47, "word": " all", "probability": 0.9453125}, {"start": 938.47, "end": 938.65, "word": " the", "probability": 0.85009765625}, {"start": 938.65, "end": 939.11, "word": " students", "probability": 0.97412109375}, {"start": 939.11, "end": 940.25, "word": " scored", "probability": 0.8486328125}, {"start": 940.25, "end": 940.73, "word": " between", "probability": 0.88232421875}, {"start": 940.73, "end": 943.23, "word": " 75", "probability": 0.9306640625}, {"start": 943.23, "end": 943.71, "word": " minus", "probability": 0.97021484375}, {"start": 943.71, "end": 944.05, "word": " 3", "probability": 0.71533203125}, {"start": 944.05, "end": 944.35, "word": " times", "probability": 0.90087890625}, {"start": 944.35, "end": 944.61, "word": " Y.", "probability": 0.290283203125}], "temperature": 1.0}, {"id": 37, "seek": 97179, "start": 946.31, "end": 971.79, "text": " and 75 plus three times one. So that's six days in two nights. Now let's look carefully at these three intervals. The first one is seven to eight, the other one 65 to 85, then six to 90. 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So this is the widest interval. Because here, the length of the interval is around 10. The other one is 20. Here is 30. So the last interval has the highest width. 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So that's another example of empirical load. And again, here we assume the data is bell shape. 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I mean, if we have data and that data is not symmetric. So that rule is no longer valid. So we have to use another rule. It's called shape-example rule.", "tokens": [281, 1071, 472, 562, 264, 1412, 307, 406, 294, 3909, 13, 286, 914, 11, 498, 321, 362, 1412, 293, 300, 1412, 307, 406, 32330, 13, 407, 300, 4978, 307, 572, 2854, 7363, 13, 407, 321, 362, 281, 764, 1071, 4978, 13, 467, 311, 1219, 3909, 12, 3121, 335, 781, 4978, 13], "avg_logprob": -0.2854567301961092, "compression_ratio": 1.5307692307692307, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 1030.08, "end": 1030.4, "word": " to", "probability": 0.19482421875}, {"start": 1030.4, "end": 1031.02, "word": " another", "probability": 0.90673828125}, {"start": 1031.02, "end": 1031.32, "word": " one", "probability": 0.92431640625}, {"start": 1031.32, "end": 1031.62, "word": " when", "probability": 0.76416015625}, {"start": 1031.62, "end": 1032.34, "word": " the", "probability": 0.75439453125}, {"start": 1032.34, "end": 1032.74, "word": " data", "probability": 0.90185546875}, {"start": 1032.74, "end": 1033.46, "word": " is", "probability": 0.9423828125}, {"start": 1033.46, "end": 1034.42, "word": " not", "probability": 0.90966796875}, {"start": 1034.42, "end": 1034.58, "word": " in", "probability": 0.1075439453125}, {"start": 1034.58, "end": 1034.84, "word": " shape.", "probability": 0.8037109375}, {"start": 1034.96, "end": 1035.08, "word": " I", "probability": 0.8935546875}, {"start": 1035.08, "end": 1035.32, "word": " mean,", "probability": 0.96435546875}, {"start": 1035.6, "end": 1036.52, "word": " if", "probability": 0.9541015625}, {"start": 1036.52, "end": 1036.66, "word": " we", "probability": 0.44873046875}, {"start": 1036.66, "end": 1036.8, "word": " have", "probability": 0.94482421875}, {"start": 1036.8, "end": 1037.2, "word": " data", "probability": 0.93994140625}, {"start": 1037.2, "end": 1038.32, "word": " and", "probability": 0.57470703125}, {"start": 1038.32, "end": 1038.56, "word": " that", "probability": 0.9365234375}, {"start": 1038.56, "end": 1038.88, "word": " data", "probability": 0.9326171875}, {"start": 1038.88, "end": 1039.1, "word": " is", "probability": 0.9482421875}, {"start": 1039.1, "end": 1039.3, "word": " not", "probability": 0.947265625}, {"start": 1039.3, "end": 1039.74, "word": " symmetric.", "probability": 0.56005859375}, {"start": 1041.74, "end": 1041.84, "word": " So", "probability": 0.493896484375}, {"start": 1041.84, "end": 1042.14, "word": " that", "probability": 0.81689453125}, {"start": 1042.14, "end": 1042.46, "word": " rule", "probability": 0.81689453125}, {"start": 1042.46, "end": 1042.66, "word": " is", "probability": 0.94970703125}, {"start": 1042.66, "end": 1042.88, "word": " no", "probability": 0.939453125}, {"start": 1042.88, "end": 1043.16, "word": " longer", "probability": 0.92578125}, {"start": 1043.16, "end": 1043.56, "word": " valid.", "probability": 0.93310546875}, {"start": 1043.72, "end": 1043.84, "word": " So", "probability": 0.94287109375}, {"start": 1043.84, "end": 1043.96, "word": " we", "probability": 0.8701171875}, {"start": 1043.96, "end": 1044.1, "word": " have", "probability": 0.9443359375}, {"start": 1044.1, "end": 1044.22, "word": " to", "probability": 0.9658203125}, {"start": 1044.22, "end": 1044.44, "word": " use", "probability": 0.87451171875}, {"start": 1044.44, "end": 1044.82, "word": " another", "probability": 0.92333984375}, {"start": 1044.82, "end": 1045.2, "word": " rule.", "probability": 0.93212890625}, {"start": 1045.9, "end": 1046.2, "word": " It's", "probability": 0.96142578125}, {"start": 1046.2, "end": 1046.66, "word": " called", "probability": 0.88720703125}, {"start": 1046.66, "end": 1047.26, "word": " shape", "probability": 0.7001953125}, {"start": 1047.26, "end": 1047.72, "word": "-example", "probability": 0.563507080078125}, {"start": 1047.72, "end": 1047.94, "word": " rule.", "probability": 0.8779296875}], "temperature": 1.0}, {"id": 41, "seek": 108291, "start": 1057.45, "end": 1082.91, "text": " Any questions before we move to the next topic? At shape and shape rule, it says that regardless of how the data are distributed, I mean, if the data is not symmetric or not bell-shaped, then we can say that at least", "tokens": [2639, 1651, 949, 321, 1286, 281, 264, 958, 4829, 30, 1711, 3909, 293, 3909, 4978, 11, 309, 1619, 300, 10060, 295, 577, 264, 1412, 366, 12631, 11, 286, 914, 11, 498, 264, 1412, 307, 406, 32330, 420, 406, 4549, 12, 23103, 11, 550, 321, 393, 584, 300, 412, 1935], "avg_logprob": -0.22796875447034837, "compression_ratio": 1.4466666666666668, "no_speech_prob": 0.0, "words": [{"start": 1057.45, "end": 1057.69, "word": " Any", "probability": 0.85205078125}, {"start": 1057.69, "end": 1058.03, "word": " questions", "probability": 0.580078125}, {"start": 1058.03, "end": 1059.33, "word": " before", "probability": 0.546875}, {"start": 1059.33, "end": 1059.79, "word": " we", "probability": 0.95458984375}, {"start": 1059.79, "end": 1060.35, "word": " move", "probability": 0.93310546875}, {"start": 1060.35, "end": 1060.53, "word": " to", "probability": 0.92822265625}, {"start": 1060.53, "end": 1060.71, "word": " the", "probability": 0.91552734375}, {"start": 1060.71, "end": 1060.99, "word": " next", "probability": 0.94140625}, {"start": 1060.99, "end": 1061.61, "word": " topic?", "probability": 0.93994140625}, {"start": 1064.39, "end": 1064.71, "word": " At", "probability": 0.26513671875}, {"start": 1064.71, "end": 1064.89, "word": " shape", "probability": 0.65380859375}, {"start": 1064.89, "end": 1065.01, "word": " and", "probability": 0.6064453125}, {"start": 1065.01, "end": 1065.21, "word": " shape", "probability": 0.66552734375}, {"start": 1065.21, "end": 1065.45, "word": " rule,", "probability": 0.468505859375}, {"start": 1065.63, "end": 1065.71, "word": " it", "probability": 0.93017578125}, {"start": 1065.71, "end": 1065.95, "word": " says", "probability": 0.87646484375}, {"start": 1065.95, "end": 1066.25, "word": " that", "probability": 0.89208984375}, {"start": 1066.25, "end": 1068.15, "word": " regardless", "probability": 0.7509765625}, {"start": 1068.15, "end": 1069.21, "word": " of", "probability": 0.96435546875}, {"start": 1069.21, "end": 1069.49, "word": " how", "probability": 0.935546875}, {"start": 1069.49, "end": 1069.69, "word": " the", "probability": 0.91796875}, {"start": 1069.69, "end": 1070.01, "word": " data", "probability": 0.94921875}, {"start": 1070.01, "end": 1070.33, "word": " are", "probability": 0.92822265625}, {"start": 1070.33, "end": 1071.03, "word": " distributed,", "probability": 0.91845703125}, {"start": 1072.07, "end": 1072.29, "word": " I", "probability": 0.814453125}, {"start": 1072.29, "end": 1072.47, "word": " mean,", "probability": 0.96630859375}, {"start": 1073.47, "end": 1073.75, "word": " if", "probability": 0.94873046875}, {"start": 1073.75, "end": 1073.89, "word": " the", "probability": 0.91748046875}, {"start": 1073.89, "end": 1074.11, "word": " data", "probability": 0.943359375}, {"start": 1074.11, "end": 1074.31, "word": " is", "probability": 0.89892578125}, {"start": 1074.31, "end": 1074.53, "word": " not", "probability": 0.9423828125}, {"start": 1074.53, "end": 1074.99, "word": " symmetric", "probability": 0.806640625}, {"start": 1074.99, "end": 1078.19, "word": " or", "probability": 0.71728515625}, {"start": 1078.19, "end": 1078.51, "word": " not", "probability": 0.9365234375}, {"start": 1078.51, "end": 1078.75, "word": " bell", "probability": 0.7421875}, {"start": 1078.75, "end": 1079.19, "word": "-shaped,", "probability": 0.720703125}, {"start": 1080.05, "end": 1080.35, "word": " then", "probability": 0.8466796875}, {"start": 1080.35, "end": 1080.53, "word": " we", "probability": 0.9501953125}, {"start": 1080.53, "end": 1080.75, "word": " can", "probability": 0.94482421875}, {"start": 1080.75, "end": 1080.95, "word": " say", "probability": 0.94384765625}, {"start": 1080.95, "end": 1081.23, "word": " that", "probability": 0.93701171875}, {"start": 1081.23, "end": 1082.51, "word": " at", "probability": 0.7900390625}, {"start": 1082.51, "end": 1082.91, "word": " least", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 42, "seek": 111067, "start": 1085.15, "end": 1110.67, "text": " Instead of saying 68, 95, or 99.7, just say around 1 minus 1 over k squared. 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In this case, we assume that k is greater than 1. I mean, you cannot apply this rule if k equals 1. 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{"id": 47, "seek": 125067, "start": 1221.85, "end": 1250.67, "text": " For bell shape, you are 95% confident there. But here, you're just 75% confident. Suppose k is 3. Now for k equal 3, we said 99.7% of the data falls within three standard deviations. 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One-ninth is 0.11. 1 minus 0.11 means 89% of the data, instead of saying 99.7. 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So here, we have two scenarios. One, if the data is symmetric, which is called empirical rule 68959917. And the other one is called shape-by-shape rule, and that regardless of the shape of the data.", "tokens": [10060, 295, 577, 264, 1412, 366, 12631, 926, 552, 13, 407, 510, 11, 321, 362, 732, 15077, 13, 1485, 11, 498, 264, 1412, 307, 32330, 11, 597, 307, 1219, 31886, 4978, 23317, 15718, 8494, 7773, 13, 400, 264, 661, 472, 307, 1219, 3909, 12, 2322, 12, 82, 42406, 4978, 11, 293, 300, 10060, 295, 264, 3909, 295, 264, 1412, 13], "avg_logprob": -0.22643443013800948, "compression_ratio": 1.526946107784431, "no_speech_prob": 0.0, "words": [{"start": 1278.51, "end": 1279.03, "word": " regardless", "probability": 0.4345703125}, {"start": 1279.03, "end": 1279.55, "word": " of", "probability": 0.95703125}, {"start": 1279.55, "end": 1279.83, "word": " how", "probability": 0.93017578125}, {"start": 1279.83, "end": 1280.03, "word": " the", "probability": 0.91943359375}, {"start": 1280.03, "end": 1280.41, "word": " data", "probability": 0.95068359375}, {"start": 1280.41, "end": 1281.37, "word": " are", "probability": 0.93798828125}, {"start": 1281.37, "end": 1282.07, "word": " distributed", "probability": 0.91796875}, {"start": 1282.07, "end": 1282.61, "word": " around", "probability": 0.93994140625}, {"start": 1282.61, "end": 1282.81, "word": " them.", "probability": 0.646484375}, {"start": 1283.33, "end": 1283.83, "word": " So", "probability": 0.92626953125}, {"start": 1283.83, "end": 1284.09, "word": " here,", "probability": 0.7255859375}, {"start": 1284.19, "end": 1284.29, "word": " we", "probability": 0.96044921875}, {"start": 1284.29, "end": 1284.47, "word": " have", "probability": 0.9453125}, {"start": 1284.47, "end": 1284.63, "word": " two", "probability": 0.89794921875}, {"start": 1284.63, "end": 1285.11, "word": " scenarios.", "probability": 0.90087890625}, {"start": 1285.73, "end": 1286.03, "word": " One,", "probability": 0.923828125}, {"start": 1286.13, "end": 1286.23, "word": " if", "probability": 0.94677734375}, {"start": 1286.23, "end": 1286.35, "word": " the", "probability": 0.91015625}, {"start": 1286.35, "end": 1286.55, "word": " data", "probability": 0.9423828125}, {"start": 1286.55, "end": 1286.75, "word": " is", "probability": 0.93408203125}, {"start": 1286.75, "end": 1287.13, "word": " symmetric,", "probability": 0.79833984375}, {"start": 1288.07, "end": 1288.31, "word": " which", "probability": 0.403076171875}, {"start": 1288.31, "end": 1288.39, "word": " is", "probability": 0.9462890625}, {"start": 1288.39, "end": 1288.63, "word": " called", "probability": 0.904296875}, {"start": 1288.63, "end": 1289.01, "word": " empirical", "probability": 0.67529296875}, {"start": 1289.01, "end": 1289.39, "word": " rule", "probability": 0.88720703125}, {"start": 1289.39, "end": 1291.41, "word": " 68959917.", "probability": 0.8505859375}, {"start": 1292.37, "end": 1292.83, "word": " And", "probability": 0.93310546875}, {"start": 1292.83, "end": 1292.93, "word": " the", "probability": 0.89404296875}, {"start": 1292.93, "end": 1293.13, "word": " other", "probability": 0.884765625}, {"start": 1293.13, "end": 1293.33, "word": " one", "probability": 0.921875}, {"start": 1293.33, "end": 1293.51, "word": " is", "probability": 0.94189453125}, {"start": 1293.51, "end": 1293.97, "word": " called", "probability": 0.892578125}, {"start": 1293.97, "end": 1294.53, "word": " shape", "probability": 0.84912109375}, {"start": 1294.53, "end": 1294.71, "word": "-by", "probability": 0.4078369140625}, {"start": 1294.71, "end": 1294.91, "word": "-shape", "probability": 0.9104817708333334}, {"start": 1294.91, "end": 1295.27, "word": " rule,", "probability": 0.89501953125}, {"start": 1296.01, "end": 1296.19, "word": " and", "probability": 0.908203125}, {"start": 1296.19, "end": 1296.45, "word": " that", "probability": 0.73974609375}, {"start": 1296.45, "end": 1297.01, "word": " regardless", "probability": 0.59423828125}, {"start": 1297.01, "end": 1297.59, "word": " of", "probability": 0.96630859375}, {"start": 1297.59, "end": 1297.79, "word": " the", "probability": 0.91259765625}, {"start": 1297.79, "end": 1298.13, "word": " shape", "probability": 0.9111328125}, {"start": 1298.13, "end": 1298.37, "word": " of", "probability": 0.96875}, {"start": 1298.37, "end": 1298.49, "word": " the", "probability": 0.91845703125}, {"start": 1298.49, "end": 1298.71, "word": " data.", "probability": 0.888671875}], "temperature": 1.0}, {"id": 50, "seek": 132983, "start": 1301.89, "end": 1329.83, "text": " Excuse me? Yes. In this case, you don't know the distribution of the data. And the reality is sometimes the data has unknown distribution. For this reason, we have to use chip-chip portions. That's all for empirical rule and chip-chip rule.", "tokens": [11359, 385, 30, 1079, 13, 682, 341, 1389, 11, 291, 500, 380, 458, 264, 7316, 295, 264, 1412, 13, 400, 264, 4103, 307, 2171, 264, 1412, 575, 9841, 7316, 13, 1171, 341, 1778, 11, 321, 362, 281, 764, 11409, 12, 339, 647, 25070, 13, 663, 311, 439, 337, 31886, 4978, 293, 11409, 12, 339, 647, 4978, 13], "avg_logprob": -0.20757004207578197, "compression_ratio": 1.4695121951219512, "no_speech_prob": 0.0, "words": [{"start": 1301.89, "end": 1302.25, "word": " Excuse", "probability": 0.552734375}, {"start": 1302.25, "end": 1302.43, "word": " me?", "probability": 0.966796875}, {"start": 1304.99, "end": 1305.63, "word": " Yes.", "probability": 0.159423828125}, {"start": 1307.19, "end": 1307.31, "word": " In", "probability": 0.7197265625}, {"start": 1307.31, "end": 1307.47, "word": " this", "probability": 0.9228515625}, {"start": 1307.47, "end": 1307.71, "word": " case,", "probability": 0.91357421875}, {"start": 1308.03, "end": 1308.39, "word": " you", "probability": 0.9580078125}, {"start": 1308.39, "end": 1308.67, "word": " don't", "probability": 0.97607421875}, {"start": 1308.67, "end": 1308.93, "word": " know", "probability": 0.900390625}, {"start": 1308.93, "end": 1309.21, "word": " the", "probability": 0.92041015625}, {"start": 1309.21, "end": 1309.87, "word": " distribution", "probability": 0.8515625}, {"start": 1309.87, "end": 1310.07, "word": " of", "probability": 0.96728515625}, {"start": 1310.07, "end": 1310.19, "word": " the", "probability": 0.9130859375}, {"start": 1310.19, "end": 1310.47, "word": " data.", "probability": 0.94189453125}, {"start": 1310.61, "end": 1310.75, "word": " And", "probability": 0.86376953125}, {"start": 1310.75, "end": 1310.91, "word": " the", "probability": 0.55517578125}, {"start": 1310.91, "end": 1311.25, "word": " reality", "probability": 0.96826171875}, {"start": 1311.25, "end": 1311.49, "word": " is", "probability": 0.79931640625}, {"start": 1311.49, "end": 1311.97, "word": " sometimes", "probability": 0.76416015625}, {"start": 1311.97, "end": 1313.09, "word": " the", "probability": 0.67138671875}, {"start": 1313.09, "end": 1313.79, "word": " data", "probability": 0.9326171875}, {"start": 1313.79, "end": 1315.29, "word": " has", "probability": 0.9248046875}, {"start": 1315.29, "end": 1316.67, "word": " unknown", "probability": 0.90625}, {"start": 1316.67, "end": 1317.95, "word": " distribution.", "probability": 0.8662109375}, {"start": 1318.37, "end": 1318.65, "word": " For", "probability": 0.962890625}, {"start": 1318.65, "end": 1318.87, "word": " this", "probability": 0.94189453125}, {"start": 1318.87, "end": 1319.13, "word": " reason,", "probability": 0.97021484375}, {"start": 1319.17, "end": 1319.29, "word": " we", "probability": 0.947265625}, {"start": 1319.29, "end": 1319.45, "word": " have", "probability": 0.94140625}, {"start": 1319.45, "end": 1319.57, "word": " to", "probability": 0.96435546875}, {"start": 1319.57, "end": 1319.93, "word": " use", "probability": 0.8740234375}, {"start": 1319.93, "end": 1320.69, "word": " chip", "probability": 0.09423828125}, {"start": 1320.69, "end": 1321.07, "word": "-chip", "probability": 0.7648111979166666}, {"start": 1321.07, "end": 1322.59, "word": " portions.", "probability": 0.385009765625}, {"start": 1325.41, "end": 1326.05, "word": " That's", "probability": 0.931396484375}, {"start": 1326.05, "end": 1326.37, "word": " all", "probability": 0.94775390625}, {"start": 1326.37, "end": 1326.93, "word": " for", "probability": 0.94384765625}, {"start": 1326.93, "end": 1328.39, "word": " empirical", "probability": 0.89404296875}, {"start": 1328.39, "end": 1328.75, "word": " rule", "probability": 0.7236328125}, {"start": 1328.75, "end": 1329.05, "word": " and", "probability": 0.9306640625}, {"start": 1329.05, "end": 1329.27, "word": " chip", "probability": 0.94775390625}, {"start": 1329.27, "end": 1329.59, "word": "-chip", "probability": 0.95361328125}, {"start": 1329.59, "end": 1329.83, "word": " rule.", "probability": 0.859375}], "temperature": 1.0}, {"id": 51, "seek": 135889, "start": 1331.23, "end": 1358.89, "text": " The next topic is quartile measures. So far, we have discussed central tendency measures, and we have talked about mean, median, and more. Then we moved to location of variability or spread or dispersion. And we talked about range, variance, and standardization.", "tokens": [440, 958, 4829, 307, 20837, 794, 8000, 13, 407, 1400, 11, 321, 362, 7152, 5777, 18187, 8000, 11, 293, 321, 362, 2825, 466, 914, 11, 26779, 11, 293, 544, 13, 1396, 321, 4259, 281, 4914, 295, 35709, 420, 3974, 420, 24631, 313, 13, 400, 321, 2825, 466, 3613, 11, 21977, 11, 293, 3832, 2144, 13], "avg_logprob": -0.17954798814441478, "compression_ratio": 1.5470588235294118, "no_speech_prob": 0.0, "words": [{"start": 1331.23, "end": 1331.51, "word": " The", "probability": 0.61669921875}, {"start": 1331.51, "end": 1331.81, "word": " next", "probability": 0.9443359375}, {"start": 1331.81, "end": 1332.31, "word": " topic", "probability": 0.95458984375}, {"start": 1332.31, "end": 1334.65, "word": " is", "probability": 0.9345703125}, {"start": 1334.65, "end": 1336.03, "word": " quartile", "probability": 0.91259765625}, {"start": 1336.03, "end": 1336.35, "word": " measures.", "probability": 0.82470703125}, {"start": 1337.19, "end": 1337.63, "word": " So", "probability": 0.970703125}, {"start": 1337.63, "end": 1337.93, "word": " far,", "probability": 0.9453125}, {"start": 1338.03, "end": 1338.15, "word": " we", "probability": 0.96337890625}, {"start": 1338.15, "end": 1338.39, "word": " have", "probability": 0.94287109375}, {"start": 1338.39, "end": 1339.47, "word": " discussed", "probability": 0.8837890625}, {"start": 1339.47, "end": 1342.41, "word": " central", "probability": 0.8642578125}, {"start": 1342.41, "end": 1342.85, "word": " tendency", "probability": 0.90185546875}, {"start": 1342.85, "end": 1343.31, "word": " measures,", "probability": 0.84814453125}, {"start": 1343.71, "end": 1344.17, "word": " and", "probability": 0.9345703125}, {"start": 1344.17, "end": 1344.33, "word": " we", "probability": 0.9638671875}, {"start": 1344.33, "end": 1344.49, "word": " have", "probability": 0.94140625}, {"start": 1344.49, "end": 1344.77, "word": " talked", "probability": 0.89453125}, {"start": 1344.77, "end": 1345.31, "word": " about", "probability": 0.91162109375}, {"start": 1345.31, "end": 1345.85, "word": " mean,", "probability": 0.8388671875}, {"start": 1346.21, "end": 1346.21, "word": " median,", "probability": 0.9365234375}, {"start": 1346.35, "end": 1346.69, "word": " and", "probability": 0.53271484375}, {"start": 1346.69, "end": 1346.83, "word": " more.", "probability": 0.88427734375}, {"start": 1347.95, "end": 1348.27, "word": " Then", "probability": 0.64794921875}, {"start": 1348.27, "end": 1348.45, "word": " we", "probability": 0.74267578125}, {"start": 1348.45, "end": 1348.81, "word": " moved", "probability": 0.67431640625}, {"start": 1348.81, "end": 1349.35, "word": " to", "probability": 0.9609375}, {"start": 1349.35, "end": 1350.27, "word": " location", "probability": 0.7060546875}, {"start": 1350.27, "end": 1350.63, "word": " of", "probability": 0.88720703125}, {"start": 1350.63, "end": 1351.21, "word": " variability", "probability": 0.97509765625}, {"start": 1351.21, "end": 1351.65, "word": " or", "probability": 0.73681640625}, {"start": 1351.65, "end": 1352.11, "word": " spread", "probability": 0.88818359375}, {"start": 1352.11, "end": 1352.83, "word": " or", "probability": 0.6572265625}, {"start": 1352.83, "end": 1353.43, "word": " dispersion.", "probability": 0.9482421875}, {"start": 1353.61, "end": 1354.29, "word": " And", "probability": 0.94580078125}, {"start": 1354.29, "end": 1354.43, "word": " we", "probability": 0.95654296875}, {"start": 1354.43, "end": 1354.69, "word": " talked", "probability": 0.771484375}, {"start": 1354.69, "end": 1355.25, "word": " about", "probability": 0.896484375}, {"start": 1355.25, "end": 1356.57, "word": " range,", "probability": 0.87548828125}, {"start": 1357.29, "end": 1357.81, "word": " variance,", "probability": 0.8896484375}, {"start": 1357.95, "end": 1358.21, "word": " and", "probability": 0.94580078125}, {"start": 1358.21, "end": 1358.89, "word": " standardization.", "probability": 0.7275390625}], "temperature": 1.0}, {"id": 52, "seek": 138715, "start": 1361.57, "end": 1387.15, "text": " And we said that outliers affect the mean much more than the median. And also, outliers affect the range. Here, we'll talk about other measures of the data, which is called quartile measures. Here, actually, we'll talk about two measures. 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So we have two measures, first and third quartile. Quartiles split the rank data into four equal segments. I mean, these measures split the data you have into four equal parts.", "tokens": [400, 264, 661, 472, 307, 2636, 20837, 794, 13, 407, 321, 362, 732, 8000, 11, 700, 293, 2636, 20837, 794, 13, 2326, 446, 4680, 7472, 264, 6181, 1412, 666, 1451, 2681, 19904, 13, 286, 914, 11, 613, 8000, 7472, 264, 1412, 291, 362, 666, 1451, 2681, 3166, 13], "avg_logprob": -0.15425701530612246, "compression_ratio": 1.5970149253731343, "no_speech_prob": 0.0, "words": [{"start": 1389.33, "end": 1389.71, "word": " And", "probability": 0.68359375}, {"start": 1389.71, "end": 1389.89, "word": " the", "probability": 0.8974609375}, {"start": 1389.89, "end": 1390.13, "word": " other", "probability": 0.884765625}, {"start": 1390.13, "end": 1390.53, "word": " one", "probability": 0.92333984375}, {"start": 1390.53, "end": 1391.55, "word": " is", "probability": 0.92626953125}, {"start": 1391.55, "end": 1391.95, "word": " third", "probability": 0.7587890625}, {"start": 1391.95, "end": 1392.51, "word": " quartile.", "probability": 0.9208984375}, {"start": 1392.75, "end": 1392.85, "word": " So", "probability": 0.94970703125}, {"start": 1392.85, "end": 1393.01, "word": " we", "probability": 0.76611328125}, {"start": 1393.01, "end": 1393.17, "word": " have", "probability": 0.94287109375}, {"start": 1393.17, "end": 1393.73, "word": " two", "probability": 0.939453125}, {"start": 1393.73, "end": 1394.15, "word": " measures,", "probability": 0.751953125}, {"start": 1395.47, "end": 1396.95, "word": " first", "probability": 0.88671875}, {"start": 1396.95, "end": 1398.47, "word": " and", "probability": 0.611328125}, {"start": 1398.47, "end": 1398.79, "word": " third", "probability": 0.90478515625}, {"start": 1398.79, "end": 1399.39, "word": " quartile.", "probability": 0.954833984375}, {"start": 1400.93, "end": 1401.79, "word": " Quartiles", "probability": 0.9456380208333334}, {"start": 1401.79, "end": 1403.89, "word": " split", "probability": 0.95068359375}, {"start": 1403.89, "end": 1405.53, "word": " the", "probability": 0.9189453125}, {"start": 1405.53, "end": 1406.03, "word": " rank", "probability": 0.5888671875}, {"start": 1406.03, "end": 1406.59, "word": " data", "probability": 0.93994140625}, {"start": 1406.59, "end": 1407.33, "word": " into", "probability": 0.84375}, {"start": 1407.33, "end": 1407.79, "word": " four", "probability": 0.9375}, {"start": 1407.79, "end": 1408.31, "word": " equal", "probability": 0.58056640625}, {"start": 1408.31, "end": 1408.83, "word": " segments.", "probability": 0.72314453125}, {"start": 1410.77, "end": 1410.99, "word": " I", "probability": 0.9736328125}, {"start": 1410.99, "end": 1411.27, "word": " mean,", "probability": 0.96337890625}, {"start": 1412.57, "end": 1412.93, "word": " these", "probability": 0.79833984375}, {"start": 1412.93, "end": 1413.39, "word": " measures", "probability": 0.86474609375}, {"start": 1413.39, "end": 1414.87, "word": " split", "probability": 0.94970703125}, {"start": 1414.87, "end": 1415.07, "word": " the", "probability": 0.9208984375}, {"start": 1415.07, "end": 1415.35, "word": " data", "probability": 0.94580078125}, {"start": 1415.35, "end": 1415.57, "word": " you", "probability": 0.95166015625}, {"start": 1415.57, "end": 1415.89, "word": " have", "probability": 0.94970703125}, {"start": 1415.89, "end": 1416.33, "word": " into", "probability": 0.845703125}, {"start": 1416.33, "end": 1416.73, "word": " four", "probability": 0.94482421875}, {"start": 1416.73, "end": 1417.19, "word": " equal", "probability": 0.8349609375}, {"start": 1417.19, "end": 1417.73, "word": " parts.", "probability": 0.84423828125}], "temperature": 1.0}, {"id": 54, "seek": 145117, "start": 1422.85, "end": 1451.17, "text": " Q1 has 25% of the data fall below it. I mean 25% of the values lie below Q1. So it means 75% of the values above it. So 25 below and 75 above. But you have to be careful that the data is arranged from smallest to largest. 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So Q2 is called the median. The median, the value in the middle when we arrange the data from smallest to largest. So that means 50% of the data below and also 50% of the data above. 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If you remember, when we computed the median, first we locate the position of the median.", "tokens": [4546, 11, 321, 8825, 577, 281, 14722, 264, 26779, 11, 293, 718, 311, 536, 577, 393, 321, 14722, 700, 293, 2636, 20837, 794, 13, 759, 291, 1604, 11, 562, 321, 40610, 264, 26779, 11, 700, 321, 22370, 264, 2535, 295, 264, 26779, 13], "avg_logprob": -0.1693004322322932, "compression_ratio": 1.5511811023622046, "no_speech_prob": 0.0, "words": [{"start": 1507.87, "end": 1508.59, "word": " Before,", "probability": 0.8056640625}, {"start": 1509.19, "end": 1509.59, "word": " we", "probability": 0.94287109375}, {"start": 1509.59, "end": 1509.87, "word": " explained", "probability": 0.58349609375}, {"start": 1509.87, "end": 1510.19, "word": " how", "probability": 0.93798828125}, {"start": 1510.19, "end": 1510.33, "word": " to", "probability": 0.97314453125}, {"start": 1510.33, "end": 1510.71, "word": " compute", "probability": 0.9052734375}, {"start": 1510.71, "end": 1512.05, "word": " the", "probability": 0.87158203125}, {"start": 1512.05, "end": 1512.35, "word": " median,", "probability": 0.95361328125}, {"start": 1512.85, "end": 1513.51, "word": " and", "probability": 0.90625}, {"start": 1513.51, "end": 1513.83, "word": " let's", "probability": 0.941162109375}, {"start": 1513.83, "end": 1514.09, "word": " see", "probability": 0.8544921875}, {"start": 1514.09, "end": 1514.45, "word": " how", "probability": 0.904296875}, {"start": 1514.45, "end": 1514.75, "word": " can", "probability": 0.580078125}, {"start": 1514.75, "end": 1514.93, "word": " we", "probability": 0.943359375}, {"start": 1514.93, "end": 1515.39, "word": " compute", "probability": 0.92041015625}, {"start": 1515.39, "end": 1516.93, "word": " first", "probability": 0.70166015625}, {"start": 1516.93, "end": 1517.23, "word": " and", "probability": 0.93505859375}, {"start": 1517.23, "end": 1517.61, "word": " third", "probability": 0.94189453125}, {"start": 1517.61, "end": 1518.85, "word": " quartile.", "probability": 0.737548828125}, {"start": 1519.75, "end": 1520.41, "word": " If", "probability": 0.94873046875}, {"start": 1520.41, "end": 1520.49, "word": " you", "probability": 0.947265625}, {"start": 1520.49, "end": 1520.81, "word": " remember,", "probability": 0.8857421875}, {"start": 1521.27, "end": 1521.47, "word": " when", "probability": 0.9169921875}, {"start": 1521.47, "end": 1521.63, "word": " we", "probability": 0.9541015625}, {"start": 1521.63, "end": 1522.05, "word": " computed", "probability": 0.91943359375}, {"start": 1522.05, "end": 1522.49, "word": " the", "probability": 0.91015625}, {"start": 1522.49, "end": 1523.65, "word": " median,", "probability": 0.97119140625}, {"start": 1524.35, "end": 1524.63, "word": " first", "probability": 0.88330078125}, {"start": 1524.63, "end": 1524.81, "word": " we", "probability": 0.759765625}, {"start": 1524.81, "end": 1525.33, "word": " locate", "probability": 0.70361328125}, {"start": 1525.33, "end": 1525.65, "word": " the", "probability": 0.89501953125}, {"start": 1525.65, "end": 1526.01, "word": " position", "probability": 0.94580078125}, {"start": 1526.01, "end": 1526.21, "word": " of", "probability": 0.96728515625}, {"start": 1526.21, "end": 1526.35, "word": " the", "probability": 0.919921875}, {"start": 1526.35, "end": 1526.57, "word": " median.", "probability": 0.9296875}], "temperature": 1.0}, {"id": 58, "seek": 155118, "start": 1527.98, "end": 1551.18, "text": " And we said that the rank of n is odd. Yes, it was n plus 1 divided by 2. This is the location of the median, not the value. Sometimes the value may be equal to the location, but most of the time it's not. It's not the case. 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median", "probability": 0.962890625}, {"start": 1575.47, "end": 1575.87, "word": " is", "probability": 0.94384765625}, {"start": 1575.87, "end": 1576.03, "word": " n", "probability": 0.98291015625}, {"start": 1576.03, "end": 1576.21, "word": " plus", "probability": 0.95849609375}, {"start": 1576.21, "end": 1576.41, "word": " 1", "probability": 0.97412109375}, {"start": 1576.41, "end": 1576.53, "word": " over", "probability": 0.8916015625}, {"start": 1576.53, "end": 1576.85, "word": " 2.", "probability": 0.98876953125}, {"start": 1578.39, "end": 1579.05, "word": " Now,", "probability": 0.95703125}, {"start": 1579.43, "end": 1579.81, "word": " for", "probability": 0.953125}, {"start": 1579.81, "end": 1580.23, "word": " the", "probability": 0.91259765625}, {"start": 1580.23, "end": 1580.49, "word": " third", "probability": 0.85595703125}, {"start": 1580.49, "end": 1581.03, "word": " quartile", "probability": 0.955322265625}, {"start": 1581.03, "end": 1581.47, "word": " position,", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 60, "seek": 161032, "start": 1583.8, "end": 1610.32, "text": " The location is N plus 1 divided by 4 times 3. So 3 times N plus 1 divided by 4. That's how can we locate Q1, Q2, and Q3. So one more time, the median, the value in the middle, and it's located exactly at the position N plus 1 over 2 for the range data.", "tokens": [440, 4914, 307, 426, 1804, 502, 6666, 538, 1017, 1413, 805, 13, 407, 805, 1413, 426, 1804, 502, 6666, 538, 1017, 13, 663, 311, 577, 393, 321, 22370, 1249, 16, 11, 1249, 17, 11, 293, 1249, 18, 13, 407, 472, 544, 565, 11, 264, 26779, 11, 264, 2158, 294, 264, 2808, 11, 293, 309, 311, 6870, 2293, 412, 264, 2535, 426, 1804, 502, 670, 568, 337, 264, 3613, 1412, 13], "avg_logprob": -0.1592209515437274, "compression_ratio": 1.5974842767295598, "no_speech_prob": 0.0, "words": [{"start": 1583.8, "end": 1584.0, "word": " The", "probability": 0.69775390625}, {"start": 1584.0, "end": 1584.4, "word": " location", "probability": 0.88623046875}, {"start": 1584.4, "end": 1584.98, "word": " is", "probability": 0.9462890625}, {"start": 1584.98, "end": 1586.7, "word": " N", "probability": 0.42431640625}, {"start": 1586.7, "end": 1586.96, "word": " plus", "probability": 0.82080078125}, {"start": 1586.96, "end": 1587.16, "word": " 1", "probability": 0.5390625}, {"start": 1587.16, "end": 1587.44, "word": " divided", "probability": 0.783203125}, {"start": 1587.44, "end": 1587.62, "word": " by", "probability": 0.96044921875}, {"start": 1587.62, "end": 1587.96, "word": " 4", "probability": 0.859375}, {"start": 1587.96, "end": 1588.32, "word": " times", "probability": 0.826171875}, {"start": 1588.32, "end": 1588.64, "word": " 3.", "probability": 0.93359375}, {"start": 1588.82, "end": 1588.98, "word": " So", "probability": 0.96044921875}, {"start": 1588.98, "end": 1589.24, "word": " 3", "probability": 0.583984375}, {"start": 1589.24, "end": 1589.76, "word": " times", "probability": 0.91357421875}, {"start": 1589.76, "end": 1590.22, "word": " N", "probability": 0.95654296875}, {"start": 1590.22, "end": 1590.46, "word": " plus", "probability": 0.95458984375}, {"start": 1590.46, "end": 1590.78, "word": " 1", "probability": 0.99267578125}, {"start": 1590.78, "end": 1591.16, "word": " divided", "probability": 0.7783203125}, {"start": 1591.16, "end": 1591.36, "word": " by", "probability": 0.95947265625}, {"start": 1591.36, "end": 1591.7, "word": " 4.", "probability": 0.97900390625}, {"start": 1592.06, "end": 1592.54, "word": " That's", "probability": 0.866943359375}, {"start": 1592.54, "end": 1592.76, "word": " how", "probability": 0.86962890625}, {"start": 1592.76, "end": 1593.0, "word": " can", "probability": 0.79150390625}, {"start": 1593.0, "end": 1593.2, "word": " we", "probability": 0.9482421875}, {"start": 1593.2, "end": 1593.8, "word": " locate", "probability": 0.93017578125}, {"start": 1593.8, "end": 1594.74, "word": " Q1,", "probability": 0.7047119140625}, {"start": 1595.42, "end": 1595.96, "word": " Q2,", "probability": 0.995849609375}, {"start": 1596.2, "end": 1596.62, "word": " and", "probability": 0.9443359375}, {"start": 1596.62, "end": 1598.2, "word": " Q3.", "probability": 0.9755859375}, {"start": 1599.32, "end": 1599.92, "word": " So", "probability": 0.95654296875}, {"start": 1599.92, "end": 1600.1, "word": " one", "probability": 0.88037109375}, {"start": 1600.1, "end": 1600.26, "word": " more", "probability": 0.931640625}, {"start": 1600.26, "end": 1600.58, "word": " time,", "probability": 0.8818359375}, {"start": 1600.76, "end": 1600.94, "word": " the", "probability": 0.90087890625}, {"start": 1600.94, "end": 1601.18, "word": " median,", "probability": 0.72021484375}, {"start": 1601.52, "end": 1601.64, "word": " the", "probability": 0.9130859375}, {"start": 1601.64, "end": 1601.86, "word": " value", "probability": 0.9677734375}, {"start": 1601.86, "end": 1601.98, "word": " in", "probability": 0.8564453125}, {"start": 1601.98, "end": 1602.08, "word": " the", "probability": 0.9189453125}, {"start": 1602.08, "end": 1602.32, "word": " middle,", "probability": 0.8193359375}, {"start": 1602.6, "end": 1602.72, "word": " and", "probability": 0.6064453125}, {"start": 1602.72, "end": 1602.86, "word": " it's", "probability": 0.83984375}, {"start": 1602.86, "end": 1603.26, "word": " located", "probability": 0.93310546875}, {"start": 1603.26, "end": 1604.0, "word": " exactly", "probability": 0.87841796875}, {"start": 1604.0, "end": 1604.4, "word": " at", "probability": 0.958984375}, {"start": 1604.4, "end": 1605.5, "word": " the", "probability": 0.90966796875}, {"start": 1605.5, "end": 1605.96, "word": " position", "probability": 0.94580078125}, {"start": 1605.96, "end": 1606.26, "word": " N", "probability": 0.919921875}, {"start": 1606.26, "end": 1606.5, "word": " plus", "probability": 0.95654296875}, {"start": 1606.5, "end": 1606.7, "word": " 1", "probability": 0.986328125}, {"start": 1606.7, "end": 1606.84, "word": " over", "probability": 0.9111328125}, {"start": 1606.84, "end": 1607.16, "word": " 2", "probability": 0.98779296875}, {"start": 1607.16, "end": 1609.2, "word": " for", "probability": 0.7275390625}, {"start": 1609.2, "end": 1609.38, "word": " the", "probability": 0.91650390625}, {"start": 1609.38, "end": 1609.64, "word": " range", "probability": 0.80810546875}, {"start": 1609.64, "end": 1610.32, "word": " data.", "probability": 0.80859375}], "temperature": 1.0}, {"id": 61, "seek": 163913, "start": 1611.01, "end": 1639.13, "text": " Q1 is located at n plus one divided by four. Q3 is located at the position three times n plus one divided by four. Now, when calculating the rank position, we can use one of these rules. First, if the result of the location, I mean, is a whole number, I mean, if it is an integer.", "tokens": [1249, 16, 307, 6870, 412, 297, 1804, 472, 6666, 538, 1451, 13, 1249, 18, 307, 6870, 412, 264, 2535, 1045, 1413, 297, 1804, 472, 6666, 538, 1451, 13, 823, 11, 562, 28258, 264, 6181, 2535, 11, 321, 393, 764, 472, 295, 613, 4474, 13, 2386, 11, 498, 264, 1874, 295, 264, 4914, 11, 286, 914, 11, 307, 257, 1379, 1230, 11, 286, 914, 11, 498, 309, 307, 364, 24922, 13], "avg_logprob": -0.15746039194120487, "compression_ratio": 1.6927710843373494, "no_speech_prob": 0.0, "words": [{"start": 1611.01, "end": 1611.53, "word": " Q1", "probability": 0.6434326171875}, {"start": 1611.53, "end": 1611.69, "word": " is", "probability": 0.8994140625}, {"start": 1611.69, "end": 1612.13, "word": " located", "probability": 0.93310546875}, {"start": 1612.13, "end": 1612.59, "word": " at", "probability": 0.92724609375}, {"start": 1612.59, "end": 1612.99, "word": " n", "probability": 0.521484375}, {"start": 1612.99, "end": 1613.23, "word": " plus", "probability": 0.55517578125}, {"start": 1613.23, "end": 1613.41, "word": " one", "probability": 0.49072265625}, {"start": 1613.41, "end": 1613.65, "word": " divided", "probability": 0.78564453125}, {"start": 1613.65, "end": 1613.79, "word": " by", "probability": 0.95849609375}, {"start": 1613.79, "end": 1614.11, "word": " four.", "probability": 0.90087890625}, {"start": 1615.21, "end": 1615.73, "word": " Q3", "probability": 0.945556640625}, {"start": 1615.73, "end": 1616.05, "word": " is", "probability": 0.9326171875}, {"start": 1616.05, "end": 1616.45, "word": " located", "probability": 0.91455078125}, {"start": 1616.45, "end": 1616.65, "word": " at", "probability": 0.9423828125}, {"start": 1616.65, "end": 1616.77, "word": " the", "probability": 0.8701171875}, {"start": 1616.77, "end": 1617.17, "word": " position", "probability": 0.95068359375}, {"start": 1617.17, "end": 1617.55, "word": " three", "probability": 0.87451171875}, {"start": 1617.55, "end": 1618.03, "word": " times", "probability": 0.912109375}, {"start": 1618.03, "end": 1618.29, "word": " n", "probability": 0.90869140625}, {"start": 1618.29, "end": 1618.51, "word": " plus", "probability": 0.95458984375}, {"start": 1618.51, "end": 1618.75, "word": " one", "probability": 0.9345703125}, {"start": 1618.75, "end": 1619.03, "word": " divided", "probability": 0.826171875}, {"start": 1619.03, "end": 1619.33, "word": " by", "probability": 0.96533203125}, {"start": 1619.33, "end": 1619.67, "word": " four.", "probability": 0.9228515625}, {"start": 1623.63, "end": 1624.05, "word": " Now,", "probability": 0.94189453125}, {"start": 1624.13, "end": 1624.31, "word": " when", "probability": 0.7802734375}, {"start": 1624.31, "end": 1624.95, "word": " calculating", "probability": 0.927734375}, {"start": 1624.95, "end": 1625.25, "word": " the", "probability": 0.904296875}, {"start": 1625.25, "end": 1625.47, "word": " rank", "probability": 0.90625}, {"start": 1625.47, "end": 1625.93, "word": " position,", "probability": 0.7333984375}, {"start": 1627.01, "end": 1627.23, "word": " we", "probability": 0.94775390625}, {"start": 1627.23, "end": 1627.49, "word": " can", "probability": 0.94677734375}, {"start": 1627.49, "end": 1627.73, "word": " use", "probability": 0.87890625}, {"start": 1627.73, "end": 1627.91, "word": " one", "probability": 0.92236328125}, {"start": 1627.91, "end": 1628.09, "word": " of", "probability": 0.96630859375}, {"start": 1628.09, "end": 1628.27, "word": " these", "probability": 0.67529296875}, {"start": 1628.27, "end": 1628.69, "word": " rules.", "probability": 0.77978515625}, {"start": 1630.25, "end": 1630.69, "word": " First,", "probability": 0.90673828125}, {"start": 1631.01, "end": 1633.21, "word": " if", "probability": 0.93896484375}, {"start": 1633.21, "end": 1633.37, "word": " the", "probability": 0.9150390625}, {"start": 1633.37, "end": 1633.83, "word": " result", "probability": 0.95263671875}, {"start": 1633.83, "end": 1634.69, "word": " of", "probability": 0.95947265625}, {"start": 1634.69, "end": 1634.79, "word": " the", "probability": 0.91748046875}, {"start": 1634.79, "end": 1635.19, "word": " location,", "probability": 0.85986328125}, {"start": 1635.29, "end": 1635.41, "word": " I", "probability": 0.97216796875}, {"start": 1635.41, "end": 1635.65, "word": " mean,", "probability": 0.96533203125}, {"start": 1636.51, "end": 1636.77, "word": " is", "probability": 0.90673828125}, {"start": 1636.77, "end": 1636.97, "word": " a", "probability": 0.99462890625}, {"start": 1636.97, "end": 1637.15, "word": " whole", "probability": 0.9111328125}, {"start": 1637.15, "end": 1637.51, "word": " number,", "probability": 0.939453125}, {"start": 1637.65, "end": 1637.79, "word": " I", "probability": 0.97607421875}, {"start": 1637.79, "end": 1638.01, "word": " mean,", "probability": 0.96826171875}, {"start": 1638.25, "end": 1638.41, "word": " if", "probability": 0.89404296875}, {"start": 1638.41, "end": 1638.53, "word": " it", "probability": 0.93310546875}, {"start": 1638.53, "end": 1638.63, "word": " is", "probability": 0.88330078125}, {"start": 1638.63, "end": 1638.83, "word": " an", "probability": 0.955078125}, {"start": 1638.83, "end": 1639.13, "word": " integer.", "probability": 0.86767578125}], "temperature": 1.0}, {"id": 62, "seek": 166977, "start": 1640.49, "end": 1669.77, "text": " Then the rank position is the same number. For example, suppose the rank position is four. So position number four is your quartile, either first or third or second quartile. So if the result is a whole number, then it is the rank position used. Now, if the result is a fractional half,", "tokens": [1396, 264, 6181, 2535, 307, 264, 912, 1230, 13, 1171, 1365, 11, 7297, 264, 6181, 2535, 307, 1451, 13, 407, 2535, 1230, 1451, 307, 428, 20837, 794, 11, 2139, 700, 420, 2636, 420, 1150, 20837, 794, 13, 407, 498, 264, 1874, 307, 257, 1379, 1230, 11, 550, 309, 307, 264, 6181, 2535, 1143, 13, 823, 11, 498, 264, 1874, 307, 257, 17948, 1966, 1922, 11], "avg_logprob": -0.1974431865594604, "compression_ratio": 1.8050314465408805, "no_speech_prob": 0.0, "words": [{"start": 1640.49, "end": 1641.23, "word": " Then", "probability": 0.397705078125}, {"start": 1641.23, "end": 1641.97, "word": " the", "probability": 0.490966796875}, {"start": 1641.97, "end": 1642.31, "word": " rank", "probability": 0.6748046875}, {"start": 1642.31, "end": 1643.23, "word": " position", "probability": 0.92333984375}, {"start": 1643.23, "end": 1643.89, "word": " is", "probability": 0.9189453125}, {"start": 1643.89, "end": 1644.05, "word": " the", "probability": 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0.88134765625}, {"start": 1652.37, "end": 1652.69, "word": " number", "probability": 0.88916015625}, {"start": 1652.69, "end": 1653.15, "word": " four", "probability": 0.89111328125}, {"start": 1653.15, "end": 1653.63, "word": " is", "probability": 0.921875}, {"start": 1653.63, "end": 1654.61, "word": " your", "probability": 0.89306640625}, {"start": 1654.61, "end": 1655.83, "word": " quartile,", "probability": 0.86083984375}, {"start": 1655.91, "end": 1656.09, "word": " either", "probability": 0.9111328125}, {"start": 1656.09, "end": 1656.59, "word": " first", "probability": 0.859375}, {"start": 1656.59, "end": 1656.89, "word": " or", "probability": 0.8486328125}, {"start": 1656.89, "end": 1657.31, "word": " third", "probability": 0.880859375}, {"start": 1657.31, "end": 1658.17, "word": " or", "probability": 0.497314453125}, {"start": 1658.17, "end": 1658.45, "word": " second", "probability": 0.904296875}, {"start": 1658.45, "end": 1658.97, "word": " quartile.", "probability": 0.969970703125}, {"start": 1659.99, "end": 1660.73, "word": " So", "probability": 0.896484375}, {"start": 1660.73, "end": 1661.09, "word": " if", "probability": 0.86083984375}, {"start": 1661.09, "end": 1661.25, "word": " the", "probability": 0.86865234375}, {"start": 1661.25, "end": 1661.53, "word": " result", "probability": 0.93603515625}, {"start": 1661.53, "end": 1661.73, "word": " is", "probability": 0.83349609375}, {"start": 1661.73, "end": 1661.83, "word": " a", "probability": 0.70166015625}, {"start": 1661.83, "end": 1661.99, "word": " whole", "probability": 0.9140625}, {"start": 1661.99, "end": 1662.25, "word": " number,", "probability": 0.94384765625}, {"start": 1662.35, "end": 1662.51, "word": " then", "probability": 0.8291015625}, {"start": 1662.51, "end": 1662.65, "word": " it", "probability": 0.935546875}, {"start": 1662.65, "end": 1662.85, "word": " is", "probability": 0.9296875}, {"start": 1662.85, "end": 1663.01, "word": " the", "probability": 0.4345703125}, {"start": 1663.01, "end": 1663.43, "word": " rank", "probability": 0.96240234375}, {"start": 1663.43, "end": 1663.91, "word": " position", "probability": 0.95166015625}, {"start": 1663.91, "end": 1664.37, "word": " used.", "probability": 0.34033203125}, {"start": 1665.95, "end": 1666.69, "word": " Now,", "probability": 0.94287109375}, {"start": 1667.41, "end": 1667.77, "word": " if", "probability": 0.9501953125}, {"start": 1667.77, "end": 1667.97, "word": " the", "probability": 0.912109375}, {"start": 1667.97, "end": 1668.35, "word": " result", "probability": 0.958984375}, {"start": 1668.35, "end": 1668.61, "word": " is", "probability": 0.94970703125}, {"start": 1668.61, "end": 1668.79, "word": " a", "probability": 0.9580078125}, {"start": 1668.79, "end": 1669.33, "word": " fractional", "probability": 0.780029296875}, {"start": 1669.33, "end": 1669.77, "word": " half,", "probability": 0.8095703125}], "temperature": 1.0}, {"id": 63, "seek": 169895, "start": 1670.29, "end": 1698.95, "text": " I mean if the right position is 2.5, 3.5, 4.5. In this case, average the two corresponding data values. For example, if the right position is 2.5. So the rank position is 2.5. So take the average of the corresponding values for the rank 2 and 3. 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That if the rank position is fractional. So if the result is whole number, just take it as it is. If it is a fractional half, take the corresponding data values and take the average of these two values.", "tokens": [412, 6181, 568, 11, 2158, 412, 6181, 805, 11, 550, 747, 264, 4274, 295, 264, 11760, 4190, 13, 663, 498, 264, 6181, 2535, 307, 17948, 1966, 13, 407, 498, 264, 1874, 307, 1379, 1230, 11, 445, 747, 309, 382, 309, 307, 13, 759, 309, 307, 257, 17948, 1966, 1922, 11, 747, 264, 11760, 1412, 4190, 293, 747, 264, 4274, 295, 613, 732, 4190, 13], "avg_logprob": -0.18461538461538463, "compression_ratio": 1.7961783439490446, "no_speech_prob": 0.0, "words": [{"start": 1699.28, "end": 1699.58, "word": " at", "probability": 0.2042236328125}, {"start": 1699.58, "end": 1699.82, "word": " rank", "probability": 0.9248046875}, {"start": 1699.82, "end": 1700.1, "word": " 2,", "probability": 0.44873046875}, {"start": 1701.38, "end": 1702.22, "word": " value", "probability": 0.9013671875}, {"start": 1702.22, "end": 1702.46, "word": " at", "probability": 0.92041015625}, {"start": 1702.46, 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For example, suppose the location is 2.1. So the position is 2, just round, up to the nearest integer. So that's 2. What's about if the position rank is 2.6? Just rank up to 3. So that's 3.", "tokens": [823, 11, 498, 264, 1874, 307, 406, 257, 1379, 1230, 420, 257, 14135, 295, 309, 13, 1171, 1365, 11, 7297, 264, 4914, 307, 568, 13, 16, 13, 407, 264, 2535, 307, 568, 11, 445, 3098, 11, 493, 281, 264, 23831, 24922, 13, 407, 300, 311, 568, 13, 708, 311, 466, 498, 264, 2535, 6181, 307, 568, 13, 21, 30, 1449, 6181, 493, 281, 805, 13, 407, 300, 311, 805, 13], "avg_logprob": -0.20202464410956478, "compression_ratio": 1.5460122699386503, "no_speech_prob": 0.0, "words": [{"start": 1726.77, "end": 1727.21, "word": " Now,", "probability": 0.8544921875}, {"start": 1727.59, "end": 1727.91, "word": " if", "probability": 0.94921875}, {"start": 1727.91, "end": 1728.07, "word": " the", "probability": 0.8974609375}, {"start": 1728.07, "end": 1728.43, "word": " result", "probability": 0.9404296875}, {"start": 1728.43, "end": 1728.71, "word": " is", "probability": 0.94873046875}, {"start": 1728.71, "end": 1728.95, "word": " not", "probability": 0.94580078125}, {"start": 1728.95, 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"end": 1783.58, "text": " So that's the rule you have to follow if the result is a number, a whole number, I mean integer, fraction of half, or not real number, I mean, not whole number, or fraction of half. Look at this specific example. Suppose we have this data. This is ordered array, 11, 12, up to 22. 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{"start": 1780.38, "end": 1780.96, "word": " 22.", "probability": 0.95947265625}, {"start": 1781.72, "end": 1782.2, "word": " And", "probability": 0.9375}, {"start": 1782.2, "end": 1782.48, "word": " let's", "probability": 0.966064453125}, {"start": 1782.48, "end": 1782.62, "word": " see", "probability": 0.916015625}, {"start": 1782.62, "end": 1782.78, "word": " how", "probability": 0.90185546875}, {"start": 1782.78, "end": 1782.98, "word": " can", "probability": 0.87353515625}, {"start": 1782.98, "end": 1783.14, "word": " we", "probability": 0.95458984375}, {"start": 1783.14, "end": 1783.58, "word": " compute", "probability": 0.8984375}], "temperature": 1.0}, {"id": 67, "seek": 181294, "start": 1785.12, "end": 1812.94, "text": " These measures. Look carefully here. First, let's compute the median. The median and the value in the middle. How many values we have? There are nine values. So the middle is number five. One, two, three, four, five. So 16.", "tokens": [1981, 8000, 13, 2053, 7500, 510, 13, 2386, 11, 718, 311, 14722, 264, 26779, 13, 440, 26779, 293, 264, 2158, 294, 264, 2808, 13, 1012, 867, 4190, 321, 362, 30, 821, 366, 4949, 4190, 13, 407, 264, 2808, 307, 1230, 1732, 13, 1485, 11, 732, 11, 1045, 11, 1451, 11, 1732, 13, 407, 3165, 13], "avg_logprob": -0.22656250345919812, "compression_ratio": 1.4088050314465408, "no_speech_prob": 0.0, "words": [{"start": 1785.1200000000001, "end": 1785.68, "word": " These", "probability": 0.2076416015625}, {"start": 1785.68, "end": 1786.24, "word": " measures.", "probability": 0.70556640625}, {"start": 1790.08, "end": 1790.64, "word": " Look", "probability": 0.71337890625}, {"start": 1790.64, "end": 1791.12, "word": " carefully", "probability": 0.8134765625}, {"start": 1791.12, "end": 1791.7, "word": " here.", "probability": 0.79833984375}, {"start": 1795.4, "end": 1795.96, "word": " First,", "probability": 0.84765625}, {"start": 1796.12, "end": 1796.4, "word": " let's", "probability": 0.931884765625}, {"start": 1796.4, "end": 1796.86, "word": " compute", "probability": 0.83544921875}, {"start": 1796.86, "end": 1798.24, "word": " the", "probability": 0.83203125}, {"start": 1798.24, "end": 1798.48, "word": " median.", "probability": 0.7939453125}, {"start": 1798.68, "end": 1798.9, "word": " The", "probability": 0.87841796875}, {"start": 1798.9, "end": 1799.1, "word": " median", "probability": 0.93310546875}, {"start": 1799.1, "end": 1799.26, "word": " and", "probability": 0.328369140625}, {"start": 1799.26, "end": 1799.34, "word": " the", "probability": 0.84912109375}, {"start": 1799.34, "end": 1799.52, "word": " value", "probability": 0.9638671875}, {"start": 1799.52, "end": 1799.64, "word": " in", "probability": 0.77734375}, {"start": 1799.64, "end": 1799.74, "word": " the", "probability": 0.9248046875}, {"start": 1799.74, "end": 1799.92, "word": " middle.", "probability": 0.93701171875}, {"start": 1800.82, "end": 1801.32, "word": " How", "probability": 0.95654296875}, {"start": 1801.32, "end": 1801.56, "word": " many", "probability": 0.900390625}, {"start": 1801.56, "end": 1801.82, "word": " values", "probability": 0.9228515625}, {"start": 1801.82, "end": 1802.02, "word": " we", "probability": 0.69970703125}, {"start": 1802.02, "end": 1802.36, "word": " have?", "probability": 0.94482421875}, {"start": 1802.8, "end": 1803.28, "word": " There", "probability": 0.78466796875}, {"start": 1803.28, "end": 1803.46, "word": " are", "probability": 0.947265625}, {"start": 1803.46, "end": 1803.8, "word": " nine", "probability": 0.75244140625}, {"start": 1803.8, "end": 1804.16, "word": " values.", "probability": 0.958984375}, {"start": 1805.88, "end": 1806.44, "word": " So", "probability": 0.80615234375}, {"start": 1806.44, "end": 1806.64, "word": " the", "probability": 0.7060546875}, {"start": 1806.64, "end": 1806.86, "word": " middle", "probability": 0.93310546875}, {"start": 1806.86, "end": 1807.32, "word": " is", "probability": 0.94677734375}, {"start": 1807.32, "end": 1808.92, "word": " number", "probability": 0.85498046875}, {"start": 1808.92, "end": 1809.34, "word": " five.", "probability": 0.6591796875}, {"start": 1809.84, "end": 1810.4, "word": " One,", "probability": 0.487060546875}, {"start": 1810.52, "end": 1810.6, "word": " two,", "probability": 0.94091796875}, {"start": 1810.7, "end": 1810.92, "word": " three,", "probability": 0.9423828125}, {"start": 1811.0, "end": 1811.24, "word": " four,", "probability": 0.94677734375}, {"start": 1811.36, "end": 1811.64, "word": " five.", "probability": 0.90673828125}, {"start": 1811.9, "end": 1812.28, "word": " So", "probability": 0.93212890625}, {"start": 1812.28, "end": 1812.94, "word": " 16.", "probability": 0.445556640625}], "temperature": 1.0}, {"id": 68, "seek": 184317, "start": 1814.83, "end": 1843.17, "text": " This value is the median. Now look at the values below the median. There are 4 and 4 below and above the median. Now let's see how can we compute Q1. The position of Q1, as we mentioned, is N plus 1 divided by 4. So N is 9 plus 1 divided by 4 is 2.5.", "tokens": [639, 2158, 307, 264, 26779, 13, 823, 574, 412, 264, 4190, 2507, 264, 26779, 13, 821, 366, 1017, 293, 1017, 2507, 293, 3673, 264, 26779, 13, 823, 718, 311, 536, 577, 393, 321, 14722, 1249, 16, 13, 440, 2535, 295, 1249, 16, 11, 382, 321, 2835, 11, 307, 426, 1804, 502, 6666, 538, 1017, 13, 407, 426, 307, 1722, 1804, 502, 6666, 538, 1017, 307, 568, 13, 20, 13], "avg_logprob": -0.1900669685431889, "compression_ratio": 1.5886075949367089, "no_speech_prob": 0.0, "words": [{"start": 1814.8300000000002, "end": 1815.39, "word": " This", "probability": 0.25146484375}, {"start": 1815.39, "end": 1815.87, "word": " value", "probability": 0.9560546875}, {"start": 1815.87, "end": 1817.89, "word": " is", "probability": 0.6484375}, {"start": 1817.89, "end": 1818.05, "word": " the", "probability": 0.84619140625}, {"start": 1818.05, "end": 1818.21, "word": " median.", "probability": 0.66357421875}, {"start": 1819.53, "end": 1819.81, "word": " Now", 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"probability": 0.85205078125}, {"start": 1842.47, "end": 1842.63, "word": " 2", "probability": 0.990234375}, {"start": 1842.63, "end": 1843.17, "word": ".5.", "probability": 0.990234375}], "temperature": 1.0}, {"id": 69, "seek": 187411, "start": 1845.41, "end": 1874.11, "text": " 2.5 position, it means you have to take the average of the two corresponding values, 2 and 3. So 2 and 3, so 12 plus 13 divided by 2. That gives 12.5. So this is Q1. So Q1 is 12.5. Now what's about Q3?", "tokens": [568, 13, 20, 2535, 11, 309, 1355, 291, 362, 281, 747, 264, 4274, 295, 264, 732, 11760, 4190, 11, 568, 293, 805, 13, 407, 568, 293, 805, 11, 370, 2272, 1804, 3705, 6666, 538, 568, 13, 663, 2709, 2272, 13, 20, 13, 407, 341, 307, 1249, 16, 13, 407, 1249, 16, 307, 2272, 13, 20, 13, 823, 437, 311, 466, 1249, 18, 30], "avg_logprob": -0.1383056645281613, "compression_ratio": 1.3289473684210527, "no_speech_prob": 0.0, "words": [{"start": 1845.41, "end": 1845.63, "word": " 2", "probability": 0.49609375}, {"start": 1845.63, "end": 1846.19, "word": ".5", "probability": 0.979248046875}, {"start": 1846.19, "end": 1846.65, "word": " position,", "probability": 0.84130859375}, {"start": 1846.97, "end": 1847.09, "word": " it", "probability": 0.880859375}, {"start": 1847.09, "end": 1847.47, "word": " means", "probability": 0.92724609375}, {"start": 1847.47, "end": 1848.29, "word": " you", "probability": 0.90380859375}, {"start": 1848.29, "end": 1848.71, "word": " have", "probability": 0.939453125}, {"start": 1848.71, "end": 1849.57, "word": " to", "probability": 0.95654296875}, {"start": 1849.57, "end": 1849.91, "word": " take", "probability": 0.8828125}, {"start": 1849.91, "end": 1850.33, "word": " the", "probability": 0.919921875}, {"start": 1850.33, "end": 1851.07, "word": " average", "probability": 0.8251953125}, {"start": 1851.07, "end": 1851.91, "word": " of", "probability": 0.94677734375}, {"start": 1851.91, "end": 1852.07, "word": " the", "probability": 0.8125}, {"start": 1852.07, "end": 1852.27, "word": " two", "probability": 0.88232421875}, {"start": 1852.27, "end": 1852.75, "word": " corresponding", "probability": 0.8515625}, {"start": 1852.75, "end": 1853.43, "word": " values,", "probability": 0.9638671875}, {"start": 1853.93, "end": 1854.05, "word": " 2", "probability": 0.6494140625}, {"start": 1854.05, "end": 1854.19, "word": " and", "probability": 0.9375}, {"start": 1854.19, "end": 1854.49, "word": " 3.", "probability": 0.9765625}, {"start": 1855.13, "end": 1855.77, "word": " So", "probability": 0.9541015625}, {"start": 1855.77, "end": 1856.13, "word": " 2", "probability": 0.701171875}, {"start": 1856.13, "end": 1857.03, "word": " and", "probability": 0.89599609375}, {"start": 1857.03, "end": 1857.39, "word": " 3,", "probability": 0.99462890625}, {"start": 1857.77, "end": 1857.95, "word": " so", "probability": 0.9326171875}, {"start": 1857.95, "end": 1858.41, "word": " 12", "probability": 0.958984375}, {"start": 1858.41, "end": 1858.73, "word": " plus", "probability": 0.90087890625}, {"start": 1858.73, "end": 1859.15, "word": " 13", "probability": 0.9345703125}, {"start": 1859.15, "end": 1859.37, "word": " divided", "probability": 0.720703125}, {"start": 1859.37, "end": 1859.59, "word": " by", "probability": 0.97021484375}, {"start": 1859.59, "end": 1859.93, "word": " 2.", "probability": 0.96240234375}, {"start": 1860.25, "end": 1860.63, "word": " That", "probability": 0.890625}, {"start": 1860.63, "end": 1861.01, "word": " gives", "probability": 0.90478515625}, {"start": 1861.01, "end": 1861.89, "word": " 12", "probability": 0.96875}, {"start": 1861.89, "end": 1862.35, "word": ".5.", "probability": 0.996826171875}, {"start": 1862.69, "end": 1863.01, "word": " So", "probability": 0.9560546875}, {"start": 1863.01, "end": 1864.75, "word": " this", "probability": 0.82958984375}, {"start": 1864.75, "end": 1865.39, "word": " is", "probability": 0.94873046875}, {"start": 1865.39, "end": 1868.39, "word": " Q1.", "probability": 0.764404296875}, {"start": 1868.53, "end": 1868.71, "word": " So", "probability": 0.947265625}, {"start": 1868.71, "end": 1869.15, "word": " Q1", "probability": 0.98095703125}, {"start": 1869.15, "end": 1869.47, "word": " is", "probability": 0.9228515625}, {"start": 1869.47, "end": 1869.79, "word": " 12", "probability": 0.951171875}, {"start": 1869.79, "end": 1870.25, "word": ".5.", "probability": 0.997314453125}, {"start": 1872.69, "end": 1873.17, "word": " Now", "probability": 0.9462890625}, {"start": 1873.17, "end": 1873.41, "word": " what's", "probability": 0.769775390625}, {"start": 1873.41, "end": 1873.65, "word": " about", "probability": 0.916015625}, {"start": 1873.65, "end": 1874.11, "word": " Q3?", "probability": 0.9970703125}], "temperature": 1.0}, {"id": 70, "seek": 190489, "start": 1876.11, "end": 1904.89, "text": " The Q3, the rank position, Q1 was 2.5. So Q3 should be three times that value, because it's three times A plus 1 over 4. That means the rank position is 7.5. That means you have to take the average of the 7 and 8 position. 7 and 8 is 18.", "tokens": [440, 1249, 18, 11, 264, 6181, 2535, 11, 1249, 16, 390, 568, 13, 20, 13, 407, 1249, 18, 820, 312, 1045, 1413, 300, 2158, 11, 570, 309, 311, 1045, 1413, 316, 1804, 502, 670, 1017, 13, 663, 1355, 264, 6181, 2535, 307, 1614, 13, 20, 13, 663, 1355, 291, 362, 281, 747, 264, 4274, 295, 264, 1614, 293, 1649, 2535, 13, 1614, 293, 1649, 307, 2443, 13], "avg_logprob": -0.1938189290025655, "compression_ratio": 1.5354838709677419, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1876.11, "end": 1876.33, "word": " The", "probability": 0.2489013671875}, {"start": 1876.33, "end": 1876.83, "word": " Q3,", "probability": 0.824951171875}, {"start": 1877.93, "end": 1878.21, "word": " the", "probability": 0.89697265625}, {"start": 1878.21, "end": 1878.45, "word": " rank", "probability": 0.94921875}, {"start": 1878.45, "end": 1878.89, "word": " position,", "probability": 0.95556640625}, {"start": 1880.69, "end": 1881.41, "word": " Q1", "probability": 0.95068359375}, {"start": 1881.41, "end": 1881.77, "word": " was", "probability": 0.94189453125}, {"start": 1881.77, "end": 1882.07, "word": " 2", "probability": 0.82666015625}, {"start": 1882.07, "end": 1883.91, "word": ".5.", "probability": 0.87451171875}, {"start": 1884.35, "end": 1884.61, "word": " So", "probability": 0.96533203125}, {"start": 1884.61, "end": 1885.09, "word": " Q3", "probability": 0.94775390625}, {"start": 1885.09, "end": 1885.35, "word": " should", "probability": 0.96875}, {"start": 1885.35, "end": 1885.63, "word": " be", "probability": 0.80712890625}, {"start": 1885.63, "end": 1887.81, "word": " three", "probability": 0.7158203125}, {"start": 1887.81, "end": 1888.27, "word": " times", "probability": 0.8935546875}, {"start": 1888.27, "end": 1888.53, "word": " that", "probability": 0.89453125}, {"start": 1888.53, "end": 1888.95, "word": " value,", "probability": 0.97998046875}, {"start": 1889.09, "end": 1889.37, "word": " because", "probability": 0.84130859375}, {"start": 1889.37, "end": 1889.67, "word": " it's", "probability": 0.941650390625}, {"start": 1889.67, "end": 1890.07, "word": " three", "probability": 0.748046875}, {"start": 1890.07, "end": 1890.69, "word": " times", "probability": 0.923828125}, {"start": 1890.69, "end": 1892.13, "word": " A", "probability": 0.2022705078125}, {"start": 1892.13, "end": 1892.41, "word": " plus", "probability": 0.92578125}, {"start": 1892.41, "end": 1892.59, "word": " 1", "probability": 0.64404296875}, {"start": 1892.59, "end": 1892.77, "word": " over", "probability": 0.87060546875}, {"start": 1892.77, "end": 1893.11, "word": " 4.", "probability": 0.90234375}, {"start": 1893.23, "end": 1893.49, "word": " That", "probability": 0.90673828125}, {"start": 1893.49, "end": 1893.83, "word": " means", "probability": 0.93115234375}, {"start": 1893.83, "end": 1894.27, "word": " the", "probability": 0.8671875}, {"start": 1894.27, "end": 1894.47, "word": " rank", "probability": 0.9296875}, {"start": 1894.47, "end": 1894.83, "word": " position", "probability": 0.94287109375}, {"start": 1894.83, "end": 1895.13, "word": " is", "probability": 0.94091796875}, {"start": 1895.13, "end": 1895.49, "word": " 7", "probability": 0.99072265625}, {"start": 1895.49, "end": 1896.09, "word": ".5.", "probability": 0.998779296875}, {"start": 1896.59, "end": 1896.85, "word": " That", "probability": 0.90234375}, {"start": 1896.85, "end": 1897.07, "word": " means", "probability": 0.92822265625}, {"start": 1897.07, "end": 1897.21, "word": " you", "probability": 0.92333984375}, {"start": 1897.21, "end": 1897.35, "word": " have", "probability": 0.93896484375}, {"start": 1897.35, "end": 1897.47, "word": " to", "probability": 0.96142578125}, {"start": 1897.47, "end": 1897.69, "word": " take", "probability": 0.84375}, {"start": 1897.69, "end": 1897.91, "word": " the", "probability": 0.916015625}, {"start": 1897.91, "end": 1898.27, "word": " average", "probability": 0.814453125}, {"start": 1898.27, "end": 1898.61, "word": " of", "probability": 0.96435546875}, {"start": 1898.61, "end": 1898.91, "word": " the", "probability": 0.91796875}, {"start": 1898.91, "end": 1899.41, "word": " 7", "probability": 0.5634765625}, {"start": 1899.41, "end": 1900.29, "word": " and", "probability": 0.857421875}, {"start": 1900.29, "end": 1900.57, "word": " 8", "probability": 0.93603515625}, {"start": 1900.57, "end": 1901.01, "word": " position.", "probability": 0.5673828125}, {"start": 1901.61, "end": 1901.89, "word": " 7", "probability": 0.78759765625}, {"start": 1901.89, "end": 1902.09, "word": " and", "probability": 0.9345703125}, {"start": 1902.09, "end": 1902.35, "word": " 8", "probability": 0.998046875}, {"start": 1902.35, "end": 1902.79, "word": " is", "probability": 0.94384765625}, {"start": 1902.79, "end": 1904.89, "word": " 18.", "probability": 0.39013671875}], "temperature": 1.0}, {"id": 71, "seek": 193398, "start": 1905.88, "end": 1933.98, "text": " which is 19.5. So that's Q3, 19.5. So this is Q3. This value is Q1. And this value is? Now, Q2 is the center.", "tokens": [597, 307, 1294, 13, 20, 13, 407, 300, 311, 1249, 18, 11, 1294, 13, 20, 13, 407, 341, 307, 1249, 18, 13, 639, 2158, 307, 1249, 16, 13, 400, 341, 2158, 307, 30, 823, 11, 1249, 17, 307, 264, 3056, 13], "avg_logprob": -0.16713170068604605, "compression_ratio": 1.264367816091954, "no_speech_prob": 0.0, "words": [{"start": 1905.88, "end": 1906.26, "word": " which", "probability": 0.298583984375}, {"start": 1906.26, "end": 1907.82, "word": " is", "probability": 0.943359375}, {"start": 1907.82, "end": 1910.22, "word": " 19", "probability": 0.6953125}, {"start": 1910.22, "end": 1912.28, "word": ".5.", "probability": 0.94287109375}, {"start": 1912.38, "end": 1912.5, "word": " So", "probability": 0.861328125}, {"start": 1912.5, "end": 1912.96, "word": " that's", "probability": 0.844970703125}, {"start": 1912.96, "end": 1913.5, "word": " Q3,", "probability": 0.8583984375}, {"start": 1915.24, "end": 1916.16, "word": " 19", "probability": 0.9091796875}, {"start": 1916.16, "end": 1916.64, "word": ".5.", "probability": 0.96484375}, {"start": 1920.36, "end": 1921.28, "word": " So", "probability": 0.91552734375}, {"start": 1921.28, "end": 1921.5, "word": " this", "probability": 0.9091796875}, {"start": 1921.5, "end": 1921.6, "word": " is", "probability": 0.927734375}, {"start": 1921.6, "end": 1922.04, "word": " Q3.", "probability": 0.80126953125}, {"start": 1923.18, "end": 1923.64, "word": " This", "probability": 0.8857421875}, {"start": 1923.64, "end": 1924.06, "word": " value", "probability": 0.96533203125}, {"start": 1924.06, "end": 1925.32, "word": " is", "probability": 0.88232421875}, {"start": 1925.32, "end": 1925.8, "word": " Q1.", "probability": 0.94921875}, {"start": 1928.12, "end": 1928.58, "word": " And", "probability": 0.85400390625}, {"start": 1928.58, "end": 1928.82, "word": " this", "probability": 0.9384765625}, {"start": 1928.82, "end": 1929.16, "word": " value", "probability": 0.97705078125}, {"start": 1929.16, "end": 1929.6, "word": " is?", "probability": 0.94580078125}, {"start": 1931.98, "end": 1932.9, "word": " Now,", "probability": 0.87744140625}, {"start": 1932.96, "end": 1933.3, "word": " Q2", "probability": 0.993896484375}, {"start": 1933.3, "end": 1933.54, "word": " is", "probability": 0.94384765625}, {"start": 1933.54, "end": 1933.72, "word": " the", "probability": 0.9287109375}, {"start": 1933.72, "end": 1933.98, "word": " center.", "probability": 0.91015625}], "temperature": 1.0}, {"id": 72, "seek": 196375, "start": 1934.99, "end": 1963.75, "text": " is located in the center because, as we mentioned, four below and four above. Now what's about Q1? Q1 is not in the center of the entire data. Because Q1, 12.5, so two points below and the others maybe how many above two, four, six, seven observations above it. So that means Q1 is not center. Also Q3 is not center because two observations above it and seven below it.", "tokens": [307, 6870, 294, 264, 3056, 570, 11, 382, 321, 2835, 11, 1451, 2507, 293, 1451, 3673, 13, 823, 437, 311, 466, 1249, 16, 30, 1249, 16, 307, 406, 294, 264, 3056, 295, 264, 2302, 1412, 13, 1436, 1249, 16, 11, 2272, 13, 20, 11, 370, 732, 2793, 2507, 293, 264, 2357, 1310, 577, 867, 3673, 732, 11, 1451, 11, 2309, 11, 3407, 18163, 3673, 309, 13, 407, 300, 1355, 1249, 16, 307, 406, 3056, 13, 2743, 1249, 18, 307, 406, 3056, 570, 732, 18163, 3673, 309, 293, 3407, 2507, 309, 13], "avg_logprob": -0.1866508197525273, "compression_ratio": 1.770334928229665, "no_speech_prob": 0.0, "words": [{"start": 1934.99, "end": 1935.25, "word": " is", "probability": 0.343994140625}, {"start": 1935.25, "end": 1935.61, "word": " located", "probability": 0.9091796875}, {"start": 1935.61, "end": 1935.79, "word": " in", "probability": 0.90869140625}, {"start": 1935.79, "end": 1935.91, "word": " the", "probability": 0.92138671875}, 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But if you just look at the data below the median, just focus on the data below the median, 12.5 lies exactly in the middle of the data.", "tokens": [407, 300, 1355, 1249, 16, 293, 1249, 18, 366, 8000, 295, 2107, 12, 2207, 2155, 4914, 11, 1339, 264, 26779, 307, 257, 3481, 295, 5777, 4914, 13, 583, 498, 291, 445, 574, 412, 264, 1412, 2507, 264, 26779, 11, 445, 1879, 322, 264, 1412, 2507, 264, 26779, 11, 2272, 13, 20, 9134, 2293, 294, 264, 2808, 295, 264, 1412, 13], "avg_logprob": -0.10892674326896667, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1964.82, "end": 1965.08, "word": " So", "probability": 0.916015625}, {"start": 1965.08, "end": 1965.3, "word": " that", "probability": 0.83203125}, {"start": 1965.3, "end": 1965.62, "word": " means", "probability": 0.9365234375}, {"start": 1965.62, "end": 1967.02, "word": " Q1", "probability": 0.8359375}, {"start": 1967.02, "end": 1967.14, "word": " and", "probability": 0.9013671875}, {"start": 1967.14, "end": 1967.5, "word": " Q3", "probability": 0.989501953125}, {"start": 1967.5, "end": 1967.74, "word": " are", "probability": 0.93212890625}, {"start": 1967.74, "end": 1968.2, "word": " measures", "probability": 0.87939453125}, {"start": 1968.2, "end": 1968.78, "word": " of", "probability": 0.9619140625}, {"start": 1968.78, "end": 1969.1, "word": " non", "probability": 0.955078125}, {"start": 1969.1, "end": 1969.64, "word": "-central", "probability": 0.904296875}, {"start": 1969.64, "end": 1970.26, "word": " location,", "probability": 0.77099609375}, {"start": 1970.42, "end": 1971.22, "word": " while", "probability": 0.91455078125}, {"start": 1971.22, "end": 1971.44, "word": " the", "probability": 0.9189453125}, {"start": 1971.44, "end": 1971.7, "word": " median", "probability": 0.94873046875}, {"start": 1971.7, "end": 1972.36, "word": " is", "probability": 0.9453125}, {"start": 1972.36, "end": 1972.48, "word": " a", "probability": 0.9736328125}, {"start": 1972.48, "end": 1972.74, "word": " measure", "probability": 0.88623046875}, {"start": 1972.74, "end": 1972.94, "word": " of", "probability": 0.96728515625}, {"start": 1972.94, "end": 1973.3, "word": " central", "probability": 0.90576171875}, {"start": 1973.3, "end": 1973.76, "word": " location.", "probability": 0.93701171875}, {"start": 1974.66, "end": 1974.94, "word": " But", "probability": 0.94873046875}, {"start": 1974.94, "end": 1975.12, "word": " if", "probability": 0.92724609375}, {"start": 1975.12, "end": 1975.3, "word": " you", "probability": 0.96240234375}, {"start": 1975.3, "end": 1975.64, "word": " just", "probability": 0.9091796875}, {"start": 1975.64, "end": 1976.08, "word": " look", "probability": 0.96142578125}, {"start": 1976.08, "end": 1977.34, "word": " at", "probability": 0.95361328125}, {"start": 1977.34, "end": 1977.58, "word": " the", "probability": 0.919921875}, {"start": 1977.58, "end": 1977.98, "word": " data", "probability": 0.94873046875}, {"start": 1977.98, "end": 1978.64, "word": " below", "probability": 0.919921875}, {"start": 1978.64, "end": 1979.12, "word": " the", "probability": 0.91650390625}, {"start": 1979.12, "end": 1979.4, "word": " median,", "probability": 0.9638671875}, {"start": 1981.42, "end": 1981.68, "word": " just", "probability": 0.88818359375}, {"start": 1981.68, "end": 1982.24, "word": " focus", "probability": 0.93896484375}, {"start": 1982.24, "end": 1983.56, "word": " on", "probability": 0.93701171875}, {"start": 1983.56, "end": 1983.72, "word": " the", "probability": 0.919921875}, {"start": 1983.72, "end": 1984.08, "word": " data", "probability": 0.94189453125}, {"start": 1984.08, "end": 1984.44, "word": " below", "probability": 0.8935546875}, {"start": 1984.44, "end": 1984.68, "word": " the", "probability": 0.9208984375}, {"start": 1984.68, "end": 1984.96, "word": " median,", "probability": 0.96240234375}, {"start": 1985.84, "end": 1986.1, "word": " 12", "probability": 0.6337890625}, {"start": 1986.1, "end": 1986.84, "word": ".5", "probability": 0.99365234375}, {"start": 1986.84, "end": 1987.78, "word": " lies", "probability": 0.9482421875}, {"start": 1987.78, "end": 1988.66, "word": " exactly", "probability": 0.90087890625}, {"start": 1988.66, "end": 1988.96, "word": " in", "probability": 0.94482421875}, {"start": 1988.96, "end": 1989.1, "word": " the", "probability": 0.91650390625}, {"start": 1989.1, "end": 1989.3, "word": " middle", "probability": 0.94970703125}, {"start": 1989.3, "end": 1989.46, "word": " of", "probability": 0.96142578125}, {"start": 1989.46, "end": 1989.58, "word": " the", "probability": 0.91064453125}, {"start": 1989.58, "end": 1989.84, "word": " data.", "probability": 0.91357421875}], "temperature": 1.0}, {"id": 74, "seek": 201923, "start": 1990.73, "end": 2019.23, "text": " So 12.5 is the center of the data. I mean, Q1 is the center of the data below the overall median. The overall median was 16. So the data before 16, the median for this data is 12.5, which is the first part. Similarly, if you look at the data above Q2, now 19.5.", "tokens": [407, 2272, 13, 20, 307, 264, 3056, 295, 264, 1412, 13, 286, 914, 11, 1249, 16, 307, 264, 3056, 295, 264, 1412, 2507, 264, 4787, 26779, 13, 440, 4787, 26779, 390, 3165, 13, 407, 264, 1412, 949, 3165, 11, 264, 26779, 337, 341, 1412, 307, 2272, 13, 20, 11, 597, 307, 264, 700, 644, 13, 13157, 11, 498, 291, 574, 412, 264, 1412, 3673, 1249, 17, 11, 586, 1294, 13, 20, 13], "avg_logprob": -0.13035102249824837, "compression_ratio": 1.6687898089171975, "no_speech_prob": 0.0, "words": [{"start": 1990.73, "end": 1990.99, "word": " So", "probability": 0.87060546875}, {"start": 1990.99, "end": 1991.31, "word": " 12", "probability": 0.716796875}, {"start": 1991.31, "end": 1991.89, "word": ".5", "probability": 0.992431640625}, {"start": 1991.89, "end": 1992.31, "word": " is", "probability": 0.9365234375}, {"start": 1992.31, "end": 1992.49, "word": " the", "probability": 0.9248046875}, {"start": 1992.49, "end": 1992.79, "word": " 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So Q3 is a measure of center for the data above the line. Make sense? So that's how can we compute first, second, and third part. Any questions? Yes, but it's a whole number. Whole number, it means any integer.", "tokens": [307, 6870, 294, 264, 2808, 295, 264, 1622, 13, 407, 1249, 18, 307, 257, 3481, 295, 3056, 337, 264, 1412, 3673, 264, 1622, 13, 4387, 2020, 30, 407, 300, 311, 577, 393, 321, 14722, 700, 11, 1150, 11, 293, 2636, 644, 13, 2639, 1651, 30, 1079, 11, 457, 309, 311, 257, 1379, 1230, 13, 30336, 1230, 11, 309, 1355, 604, 24922, 13], "avg_logprob": -0.2508680546094501, "compression_ratio": 1.4310344827586208, "no_speech_prob": 0.0, "words": [{"start": 2019.51, "end": 2019.79, "word": " is", "probability": 0.341796875}, {"start": 2019.79, "end": 2020.17, "word": " located", "probability": 0.93505859375}, {"start": 2020.17, "end": 2020.47, "word": " in", "probability": 0.947265625}, {"start": 2020.47, "end": 2020.61, "word": " the", "probability": 0.91748046875}, {"start": 2020.61, "end": 2020.81, "word": " middle", "probability": 0.94775390625}, {"start": 2020.81, "end": 2020.99, "word": " of", "probability": 0.88623046875}, {"start": 2020.99, "end": 2021.13, "word": " the", "probability": 0.75}, {"start": 2021.13, "end": 2021.25, "word": " line.", "probability": 0.139892578125}, {"start": 2021.89, "end": 2022.19, "word": " So", "probability": 0.9560546875}, {"start": 2022.19, "end": 2022.79, "word": " Q3", "probability": 0.777587890625}, {"start": 2022.79, "end": 2023.27, "word": " is", "probability": 0.9462890625}, {"start": 2023.27, "end": 2023.47, "word": " a", "probability": 0.9423828125}, {"start": 2023.47, "end": 2023.71, "word": " measure", "probability": 0.6171875}, {"start": 2023.71, "end": 2023.95, "word": " of", "probability": 0.900390625}, {"start": 2023.95, "end": 2024.35, "word": " center", "probability": 0.86328125}, {"start": 2024.35, "end": 2025.01, "word": " for", "probability": 0.93212890625}, {"start": 2025.01, "end": 2025.23, "word": " the", "probability": 0.90869140625}, {"start": 2025.23, "end": 2025.61, "word": " data", "probability": 0.939453125}, {"start": 2025.61, "end": 2026.25, "word": " above", "probability": 0.8759765625}, {"start": 2026.25, "end": 2026.47, "word": " the", "probability": 0.78369140625}, {"start": 2026.47, "end": 2026.63, "word": " line.", "probability": 0.74609375}, {"start": 2027.73, "end": 2028.07, "word": " Make", "probability": 0.73046875}, {"start": 2028.07, "end": 2028.39, "word": " sense?", "probability": 0.85498046875}, {"start": 2031.37, "end": 2031.97, "word": " So", "probability": 0.9296875}, {"start": 2031.97, "end": 2032.47, "word": " that's", "probability": 0.941162109375}, {"start": 2032.47, "end": 2032.77, "word": " how", "probability": 0.8876953125}, {"start": 2032.77, "end": 2033.03, "word": " can", "probability": 0.759765625}, {"start": 2033.03, "end": 2033.19, "word": " we", "probability": 0.85888671875}, {"start": 2033.19, "end": 2033.59, "word": " compute", "probability": 0.87890625}, {"start": 2033.59, "end": 2034.07, "word": " first,", "probability": 0.81103515625}, {"start": 2034.41, "end": 2035.09, "word": " second,", "probability": 0.9052734375}, {"start": 2036.15, "end": 2036.43, "word": " and", "probability": 0.93310546875}, {"start": 2036.43, "end": 2036.69, "word": " third", "probability": 0.9296875}, {"start": 2036.69, "end": 2037.01, "word": " part.", "probability": 0.214111328125}, {"start": 2038.57, "end": 2039.17, "word": " Any", "probability": 0.90234375}, {"start": 2039.17, "end": 2039.53, "word": " questions?", "probability": 0.95361328125}, {"start": 2042.13, "end": 2042.73, "word": " Yes,", "probability": 0.158447265625}, {"start": 2042.85, "end": 2042.95, "word": " but", "probability": 0.3583984375}, {"start": 2042.95, "end": 2043.21, "word": " it's", "probability": 0.635498046875}, {"start": 2043.21, "end": 2043.29, "word": " a", "probability": 0.98095703125}, {"start": 2043.29, "end": 2043.51, "word": " whole", "probability": 0.9052734375}, {"start": 2043.51, "end": 2043.83, "word": " number.", "probability": 0.9345703125}, {"start": 2044.71, "end": 2045.29, "word": " Whole", "probability": 0.84765625}, {"start": 2045.29, "end": 2045.63, "word": " number,", "probability": 0.93408203125}, {"start": 2045.67, "end": 2045.79, "word": " it", "probability": 0.92919921875}, {"start": 2045.79, "end": 2046.03, "word": " means", "probability": 0.92626953125}, {"start": 2046.03, "end": 2046.23, "word": " any", "probability": 0.52587890625}, {"start": 2046.23, "end": 2046.49, "word": " integer.", "probability": 0.93359375}], "temperature": 1.0}, {"id": 76, "seek": 207503, "start": 2048.77, "end": 2075.03, "text": " For example, yeah, exactly, yes. Suppose we have number of data is seven. Number of observations we have is seven. So the rank position n plus one divided by two, seven plus one over two is four. Four means the whole number, I mean an integer.", "tokens": [1171, 1365, 11, 1338, 11, 2293, 11, 2086, 13, 21360, 321, 362, 1230, 295, 1412, 307, 3407, 13, 5118, 295, 18163, 321, 362, 307, 3407, 13, 407, 264, 6181, 2535, 297, 1804, 472, 6666, 538, 732, 11, 3407, 1804, 472, 670, 732, 307, 1451, 13, 7451, 1355, 264, 1379, 1230, 11, 286, 914, 364, 24922, 13], "avg_logprob": -0.2219024185548749, "compression_ratio": 1.5443037974683544, "no_speech_prob": 0.0, "words": [{"start": 2048.77, "end": 2049.37, "word": " For", "probability": 0.5888671875}, {"start": 2049.37, "end": 2049.71, "word": " example,", "probability": 0.970703125}, {"start": 2049.83, "end": 2049.93, "word": " yeah,", "probability": 0.482666015625}, {"start": 2049.99, "end": 2050.25, "word": " exactly,", "probability": 0.8173828125}, {"start": 2050.39, "end": 2050.51, "word": " yes.", "probability": 0.75390625}, {"start": 2051.19, "end": 2051.79, "word": " Suppose", "probability": 0.77587890625}, {"start": 2051.79, "end": 2054.11, "word": " we", "probability": 0.62841796875}, {"start": 2054.11, "end": 2054.45, "word": " have", "probability": 0.9482421875}, {"start": 2054.45, "end": 2056.93, "word": " number", "probability": 0.64111328125}, {"start": 2056.93, "end": 2057.13, "word": " of", "probability": 0.96875}, {"start": 2057.13, "end": 2057.37, "word": " data", "probability": 0.94384765625}, {"start": 2057.37, "end": 2057.67, "word": " is", "probability": 0.8828125}, {"start": 2057.67, "end": 2058.09, "word": " seven.", "probability": 0.70068359375}, {"start": 2062.07, "end": 2062.67, "word": " Number", "probability": 0.7529296875}, {"start": 2062.67, "end": 2062.83, "word": " of", "probability": 0.95166015625}, {"start": 2062.83, "end": 2063.17, "word": " observations", "probability": 0.80126953125}, {"start": 2063.17, "end": 2063.39, "word": " we", "probability": 0.7197265625}, {"start": 2063.39, "end": 2063.53, "word": " have", "probability": 0.94677734375}, {"start": 2063.53, "end": 2063.65, "word": " is", "probability": 0.6357421875}, {"start": 2063.65, "end": 2063.89, "word": " seven.", "probability": 0.89404296875}, {"start": 2064.35, "end": 2064.73, "word": " So", "probability": 0.94921875}, {"start": 2064.73, "end": 2065.07, "word": " the", "probability": 0.60888671875}, {"start": 2065.07, "end": 2065.37, "word": " rank", "probability": 0.91796875}, {"start": 2065.37, "end": 2066.03, "word": " position", "probability": 0.9365234375}, {"start": 2066.03, "end": 2066.87, "word": " n", "probability": 0.49755859375}, {"start": 2066.87, "end": 2067.13, "word": " plus", "probability": 0.8896484375}, {"start": 2067.13, "end": 2067.33, "word": " one", "probability": 0.60888671875}, {"start": 2067.33, "end": 2067.59, "word": " divided", "probability": 0.79150390625}, {"start": 2067.59, "end": 2067.77, "word": " by", "probability": 0.97265625}, {"start": 2067.77, "end": 2068.07, "word": " two,", "probability": 0.92626953125}, {"start": 2068.99, "end": 2069.73, "word": " seven", "probability": 0.904296875}, {"start": 2069.73, "end": 2070.09, "word": " plus", "probability": 0.955078125}, {"start": 2070.09, "end": 2070.41, "word": " one", "probability": 0.93603515625}, {"start": 2070.41, "end": 2070.63, "word": " over", "probability": 0.9189453125}, {"start": 2070.63, "end": 2070.91, "word": " two", "probability": 0.94189453125}, {"start": 2070.91, "end": 2071.05, "word": " is", "probability": 0.919921875}, {"start": 2071.05, "end": 2071.35, "word": " four.", "probability": 0.94580078125}, {"start": 2072.19, "end": 2072.79, "word": " Four", "probability": 0.92822265625}, {"start": 2072.79, "end": 2073.41, "word": " means", "probability": 0.564453125}, {"start": 2073.41, "end": 2073.71, "word": " the", "probability": 0.91015625}, {"start": 2073.71, "end": 2073.89, "word": " whole", "probability": 0.88916015625}, {"start": 2073.89, "end": 2074.21, "word": " number,", "probability": 0.93310546875}, {"start": 2074.31, "end": 2074.41, "word": " I", "probability": 0.7958984375}, {"start": 2074.41, "end": 2074.55, "word": " mean", "probability": 0.966796875}, {"start": 2074.55, "end": 2074.77, "word": " an", "probability": 0.5498046875}, {"start": 2074.77, "end": 2075.03, "word": " integer.", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 77, "seek": 210176, "start": 2076.4, "end": 2101.76, "text": " then this case just use it as it is. Now let's see the benefit or the feature of using Q1 and Q3. So let's move at the inter-equilateral range or IQ1.", "tokens": [550, 341, 1389, 445, 764, 309, 382, 309, 307, 13, 823, 718, 311, 536, 264, 5121, 420, 264, 4111, 295, 1228, 1249, 16, 293, 1249, 18, 13, 407, 718, 311, 1286, 412, 264, 728, 12, 12816, 37751, 3613, 420, 28921, 16, 13], "avg_logprob": -0.30595929955327233, "compression_ratio": 1.2583333333333333, "no_speech_prob": 0.0, "words": [{"start": 2076.4, "end": 2076.74, "word": " then", "probability": 0.492431640625}, {"start": 2076.74, "end": 2077.0, "word": " this", "probability": 0.515625}, {"start": 2077.0, "end": 2077.16, "word": " case", "probability": 0.86669921875}, {"start": 2077.16, "end": 2077.46, "word": " just", "probability": 0.7568359375}, {"start": 2077.46, "end": 2077.78, "word": " use", "probability": 0.84423828125}, {"start": 2077.78, "end": 2078.18, "word": " it", "probability": 0.9384765625}, {"start": 2078.18, "end": 2079.48, "word": " as", "probability": 0.896484375}, {"start": 2079.48, "end": 2079.66, "word": " it", "probability": 0.94482421875}, {"start": 2079.66, "end": 2079.92, "word": " is.", "probability": 0.9423828125}, {"start": 2082.1, "end": 2082.32, "word": " Now", "probability": 0.50244140625}, {"start": 2082.32, "end": 2082.66, "word": " let's", "probability": 0.8837890625}, {"start": 2082.66, "end": 2082.96, "word": " see", "probability": 0.92529296875}, {"start": 2082.96, "end": 2084.3, "word": " the", "probability": 0.87158203125}, {"start": 2084.3, "end": 2084.62, "word": " benefit", "probability": 0.783203125}, {"start": 2084.62, "end": 2085.14, "word": " or", "probability": 0.90576171875}, {"start": 2085.14, "end": 2085.28, "word": " the", "probability": 0.90087890625}, {"start": 2085.28, "end": 2085.62, "word": " feature", "probability": 0.76513671875}, {"start": 2085.62, "end": 2086.44, "word": " of", "probability": 0.9384765625}, {"start": 2086.44, "end": 2086.96, "word": " using", "probability": 0.9365234375}, {"start": 2086.96, "end": 2087.94, "word": " Q1", "probability": 0.79931640625}, {"start": 2087.94, "end": 2088.14, "word": " and", "probability": 0.9287109375}, {"start": 2088.14, "end": 2088.68, "word": " Q3.", "probability": 0.99462890625}, {"start": 2095.18, "end": 2095.98, "word": " So", "probability": 0.7734375}, {"start": 2095.98, "end": 2096.5, "word": " let's", "probability": 0.929931640625}, {"start": 2096.5, "end": 2097.66, "word": " move", "probability": 0.92724609375}, {"start": 2097.66, "end": 2098.1, "word": " at", "probability": 0.89306640625}, {"start": 2098.1, "end": 2099.16, "word": " the", "probability": 0.91455078125}, {"start": 2099.16, "end": 2099.52, "word": " inter", "probability": 0.188232421875}, {"start": 2099.52, "end": 2099.88, "word": "-equilateral", "probability": 0.55419921875}, {"start": 2099.88, "end": 2100.52, "word": " range", "probability": 0.88330078125}, {"start": 2100.52, "end": 2101.3, "word": " or", "probability": 0.72607421875}, {"start": 2101.3, "end": 2101.76, "word": " IQ1.", "probability": 0.466064453125}], "temperature": 1.0}, {"id": 78, "seek": 213060, "start": 2108.02, "end": 2130.6, "text": " 2.5 is the position. So the rank data of the rank data. So take the average of the two corresponding values of this one, which is 2 and 3. So 2 and 3. The average of these two values is 12.5.", "tokens": [568, 13, 20, 307, 264, 2535, 13, 407, 264, 6181, 1412, 295, 264, 6181, 1412, 13, 407, 747, 264, 4274, 295, 264, 732, 11760, 4190, 295, 341, 472, 11, 597, 307, 568, 293, 805, 13, 407, 568, 293, 805, 13, 440, 4274, 295, 613, 732, 4190, 307, 2272, 13, 20, 13], "avg_logprob": -0.13972355941167244, "compression_ratio": 1.6, "no_speech_prob": 0.0, "words": [{"start": 2108.02, "end": 2108.7, "word": " 2", "probability": 0.431396484375}, {"start": 2108.7, "end": 2109.36, "word": ".5", "probability": 0.984130859375}, {"start": 2109.36, "end": 2110.16, "word": " is", "probability": 0.89306640625}, {"start": 2110.16, "end": 2110.32, "word": " the", "probability": 0.9052734375}, {"start": 2110.32, "end": 2110.8, "word": " position.", "probability": 0.9296875}, {"start": 2112.06, "end": 2112.74, "word": " So", "probability": 0.8857421875}, {"start": 2112.74, "end": 2113.28, "word": " the", "probability": 0.59521484375}, {"start": 2113.28, "end": 2113.56, "word": " rank", "probability": 0.87451171875}, {"start": 2113.56, "end": 2113.86, "word": " data", "probability": 0.83984375}, {"start": 2113.86, "end": 2114.2, "word": " of", "probability": 0.7490234375}, {"start": 2114.2, "end": 2114.38, "word": " the", "probability": 0.880859375}, {"start": 2114.38, "end": 2114.58, "word": " rank", "probability": 0.91845703125}, {"start": 2114.58, "end": 2114.96, "word": " data.", "probability": 0.904296875}, {"start": 2115.74, "end": 2116.02, "word": " So", "probability": 0.93896484375}, {"start": 2116.02, "end": 2116.38, "word": " take", "probability": 0.734375}, {"start": 2116.38, "end": 2117.28, "word": " the", "probability": 0.91552734375}, {"start": 2117.28, "end": 2117.84, "word": " average", "probability": 0.79052734375}, {"start": 2117.84, "end": 2118.3, "word": " of", "probability": 0.96337890625}, {"start": 2118.3, "end": 2118.48, "word": " the", "probability": 0.90576171875}, {"start": 2118.48, "end": 2118.68, "word": " two", "probability": 0.8876953125}, {"start": 2118.68, "end": 2119.18, "word": " corresponding", "probability": 0.81982421875}, {"start": 2119.18, "end": 2119.72, "word": " values", "probability": 0.9658203125}, {"start": 2119.72, "end": 2119.88, "word": " of", "probability": 0.94873046875}, {"start": 2119.88, "end": 2120.08, "word": " this", "probability": 0.9453125}, {"start": 2120.08, "end": 2120.34, "word": " one,", "probability": 0.9189453125}, {"start": 2120.42, "end": 2120.58, "word": " which", "probability": 0.93798828125}, {"start": 2120.58, "end": 2120.7, "word": " is", "probability": 0.9375}, {"start": 2120.7, "end": 2120.88, "word": " 2", "probability": 0.53515625}, {"start": 2120.88, "end": 2121.02, "word": " and", "probability": 0.931640625}, {"start": 2121.02, "end": 2121.34, "word": " 3.", "probability": 0.98974609375}, {"start": 2122.52, "end": 2122.92, "word": " So", "probability": 0.84033203125}, {"start": 2122.92, "end": 2123.96, "word": " 2", "probability": 0.7880859375}, {"start": 2123.96, "end": 2125.3, "word": " and", "probability": 0.921875}, {"start": 2125.3, "end": 2125.7, "word": " 3.", "probability": 0.99755859375}, {"start": 2127.4, "end": 2127.62, "word": " The", "probability": 0.85986328125}, {"start": 2127.62, "end": 2127.96, "word": " average", "probability": 0.78955078125}, {"start": 2127.96, "end": 2128.14, "word": " of", "probability": 0.953125}, {"start": 2128.14, "end": 2128.32, "word": " these", "probability": 0.85205078125}, {"start": 2128.32, "end": 2128.5, "word": " two", "probability": 0.9248046875}, {"start": 2128.5, "end": 2129.06, "word": " values", "probability": 0.96923828125}, {"start": 2129.06, "end": 2129.76, "word": " is", "probability": 0.93896484375}, {"start": 2129.76, "end": 2130.08, "word": " 12", "probability": 0.908203125}, {"start": 2130.08, "end": 2130.6, "word": ".5.", "probability": 0.996337890625}], "temperature": 1.0}, {"id": 79, "seek": 215952, "start": 2131.48, "end": 2159.52, "text": " One more time, 2.5 is not the value. It is the rank position of the first quartile. So in this case, 2.5 takes position 2 and 3. The average of these two rank positions", "tokens": [1485, 544, 565, 11, 568, 13, 20, 307, 406, 264, 2158, 13, 467, 307, 264, 6181, 2535, 295, 264, 700, 20837, 794, 13, 407, 294, 341, 1389, 11, 568, 13, 20, 2516, 2535, 568, 293, 805, 13, 440, 4274, 295, 613, 732, 6181, 8432], "avg_logprob": -0.14835069047080146, "compression_ratio": 1.4083333333333334, "no_speech_prob": 0.0, "words": [{"start": 2131.48, "end": 2131.74, "word": " One", "probability": 0.708984375}, {"start": 2131.74, "end": 2131.94, "word": " more", "probability": 0.93359375}, {"start": 2131.94, "end": 2132.14, "word": " time,", "probability": 0.88134765625}, {"start": 2132.28, "end": 2133.52, "word": " 2", "probability": 0.53173828125}, {"start": 2133.52, "end": 2134.12, "word": ".5", "probability": 0.99169921875}, {"start": 2134.12, "end": 2136.6, "word": " is", "probability": 0.87646484375}, {"start": 2136.6, "end": 2136.88, "word": " not", "probability": 0.94921875}, {"start": 2136.88, "end": 2137.08, "word": " the", "probability": 0.9072265625}, {"start": 2137.08, "end": 2137.38, "word": " value.", "probability": 0.9716796875}, {"start": 2139.72, "end": 2140.3, "word": " It", "probability": 0.94921875}, {"start": 2140.3, "end": 2140.48, "word": " is", "probability": 0.92626953125}, {"start": 2140.48, "end": 2140.7, "word": " the", "probability": 0.90966796875}, {"start": 2140.7, "end": 2140.92, "word": " rank", "probability": 0.95263671875}, {"start": 2140.92, "end": 2141.36, "word": " position", "probability": 0.93896484375}, {"start": 2141.36, "end": 2142.68, "word": " of", "probability": 0.94921875}, {"start": 2142.68, "end": 2143.2, "word": " the", "probability": 0.919921875}, {"start": 2143.2, "end": 2143.52, "word": " first", "probability": 0.87255859375}, {"start": 2143.52, "end": 2144.1, "word": " quartile.", "probability": 0.831787109375}, {"start": 2145.5, "end": 2145.9, "word": " So", "probability": 0.91259765625}, {"start": 2145.9, "end": 2146.04, "word": " in", "probability": 0.72607421875}, {"start": 2146.04, "end": 2146.24, "word": " this", "probability": 0.947265625}, {"start": 2146.24, "end": 2146.7, "word": " case,", "probability": 0.91552734375}, {"start": 2147.52, "end": 2147.88, "word": " 2", "probability": 0.98828125}, {"start": 2147.88, "end": 2148.5, "word": ".5", "probability": 0.998291015625}, {"start": 2148.5, "end": 2150.76, "word": " takes", "probability": 0.423583984375}, {"start": 2150.76, "end": 2152.14, "word": " position", "probability": 0.8544921875}, {"start": 2152.14, "end": 2152.6, "word": " 2", "probability": 0.5390625}, {"start": 2152.6, "end": 2153.76, "word": " and", "probability": 0.8740234375}, {"start": 2153.76, "end": 2154.12, "word": " 3.", "probability": 0.96630859375}, {"start": 2155.5, "end": 2156.42, "word": " The", "probability": 0.876953125}, {"start": 2156.42, "end": 2156.94, "word": " average", "probability": 0.7978515625}, {"start": 2156.94, "end": 2157.42, "word": " of", "probability": 0.96435546875}, {"start": 2157.42, "end": 2157.74, "word": " these", "probability": 0.8505859375}, {"start": 2157.74, "end": 2158.2, "word": " two", "probability": 0.9013671875}, {"start": 2158.2, "end": 2158.86, "word": " rank", "probability": 0.93798828125}, {"start": 2158.86, "end": 2159.52, "word": " positions", "probability": 0.86669921875}], "temperature": 1.0}, {"id": 80, "seek": 219000, "start": 2160.34, "end": 2190.0, "text": " the corresponding one, which are 12 and 13. So 12 for position number 2, 13 for the other one. So the average is just divided by 2. That will give 12.5. Next, again,", "tokens": [264, 11760, 472, 11, 597, 366, 2272, 293, 3705, 13, 407, 2272, 337, 2535, 1230, 568, 11, 3705, 337, 264, 661, 472, 13, 407, 264, 4274, 307, 445, 6666, 538, 568, 13, 663, 486, 976, 2272, 13, 20, 13, 3087, 11, 797, 11], "avg_logprob": -0.23987925560636955, "compression_ratio": 1.2868217054263567, "no_speech_prob": 0.0, "words": [{"start": 2160.34, "end": 2160.6, "word": " the", "probability": 0.22216796875}, {"start": 2160.6, "end": 2161.06, "word": " corresponding", "probability": 0.87548828125}, {"start": 2161.06, "end": 2161.48, "word": " one,", "probability": 0.5859375}, {"start": 2162.26, "end": 2162.58, "word": " which", "probability": 0.947265625}, {"start": 2162.58, "end": 2163.02, "word": " are", "probability": 0.89404296875}, {"start": 2163.02, "end": 2163.64, "word": " 12", "probability": 0.79931640625}, {"start": 2163.64, "end": 2163.94, "word": " and", "probability": 0.923828125}, {"start": 2163.94, "end": 2164.38, "word": " 13.", "probability": 0.94384765625}, {"start": 2164.86, "end": 2165.32, "word": " So", "probability": 0.92333984375}, {"start": 2165.32, "end": 2165.74, "word": " 12", "probability": 0.89453125}, {"start": 2165.74, "end": 2166.74, "word": " for", "probability": 0.8544921875}, {"start": 2166.74, "end": 2167.78, "word": " position", "probability": 0.7236328125}, {"start": 2167.78, "end": 2168.1, "word": " number", "probability": 0.94775390625}, {"start": 2168.1, "end": 2168.4, "word": " 2,", "probability": 0.55615234375}, {"start": 2169.18, "end": 2169.72, "word": " 13", "probability": 0.953125}, {"start": 2169.72, "end": 2170.08, "word": " for", "probability": 0.9501953125}, {"start": 2170.08, "end": 2170.54, "word": " the", "probability": 0.91015625}, {"start": 2170.54, "end": 2170.78, "word": " other", "probability": 0.89453125}, {"start": 2170.78, "end": 2171.02, "word": " one.", "probability": 0.9150390625}, {"start": 2171.9, "end": 2172.16, "word": " So", "probability": 0.85986328125}, {"start": 2172.16, "end": 2172.34, "word": " the", "probability": 0.88916015625}, {"start": 2172.34, "end": 2172.68, "word": " average", "probability": 0.79833984375}, {"start": 2172.68, "end": 2173.02, "word": " is", "probability": 0.28857421875}, {"start": 2173.02, "end": 2173.16, "word": " just", "probability": 0.8017578125}, {"start": 2173.16, "end": 2173.4, "word": " divided", "probability": 0.71142578125}, {"start": 2173.4, "end": 2173.58, "word": " by", "probability": 0.9697265625}, {"start": 2173.58, "end": 2173.84, "word": " 2.", "probability": 0.82958984375}, {"start": 2174.24, "end": 2174.74, "word": " That", "probability": 0.85791015625}, {"start": 2174.74, "end": 2174.94, "word": " will", "probability": 0.8779296875}, {"start": 2174.94, "end": 2175.32, "word": " give", "probability": 0.87744140625}, {"start": 2175.32, "end": 2176.1, "word": " 12", "probability": 0.87158203125}, {"start": 2176.1, "end": 2176.66, "word": ".5.", "probability": 0.9951171875}, {"start": 2188.76, "end": 2189.54, "word": " Next,", "probability": 0.5302734375}, {"start": 2189.68, "end": 2190.0, "word": " again,", "probability": 0.958984375}], "temperature": 1.0}, {"id": 81, "seek": 221906, "start": 2191.5, "end": 2219.06, "text": " the inter-quartile range, which is denoted by IQR. Now IQR is the distance between Q3 and Q1. I mean the difference between Q3 and Q1 is called the inter-quartile range. And this one measures the spread in the middle 50% of the data. Because if you imagine that,", "tokens": [264, 728, 12, 358, 446, 794, 3613, 11, 597, 307, 1441, 23325, 538, 28921, 49, 13, 823, 28921, 49, 307, 264, 4560, 1296, 1249, 18, 293, 1249, 16, 13, 286, 914, 264, 2649, 1296, 1249, 18, 293, 1249, 16, 307, 1219, 264, 728, 12, 358, 446, 794, 3613, 13, 400, 341, 472, 8000, 264, 3974, 294, 264, 2808, 2625, 4, 295, 264, 1412, 13, 1436, 498, 291, 3811, 300, 11], "avg_logprob": -0.14711708040304586, "compression_ratio": 1.5654761904761905, "no_speech_prob": 0.0, "words": [{"start": 2191.5, "end": 2191.96, "word": " the", "probability": 0.2626953125}, {"start": 2191.96, "end": 2192.28, "word": " inter", "probability": 0.4306640625}, {"start": 2192.28, "end": 2192.74, "word": "-quartile", "probability": 0.8492431640625}, {"start": 2192.74, "end": 2193.16, "word": " range,", "probability": 0.88671875}, {"start": 2193.42, "end": 2194.68, "word": " which", "probability": 0.9521484375}, {"start": 2194.68, "end": 2194.9, "word": " is", "probability": 0.9482421875}, {"start": 2194.9, "end": 2195.4, "word": " denoted", "probability": 0.953369140625}, {"start": 2195.4, "end": 2196.5, "word": " by", "probability": 0.97607421875}, {"start": 2196.5, "end": 2197.36, "word": " IQR.", "probability": 0.933349609375}, {"start": 2199.28, "end": 2199.86, "word": " Now", "probability": 0.9365234375}, {"start": 2199.86, "end": 2200.84, "word": " IQR", "probability": 0.792236328125}, {"start": 2200.84, "end": 2202.58, "word": " is", "probability": 0.88330078125}, {"start": 2202.58, "end": 2202.76, "word": " the", "probability": 0.91552734375}, {"start": 2202.76, "end": 2203.24, "word": " distance", "probability": 0.931640625}, {"start": 2203.24, "end": 2203.68, "word": " between", "probability": 0.876953125}, {"start": 2203.68, "end": 2204.16, "word": " Q3", "probability": 0.902587890625}, {"start": 2204.16, "end": 2204.34, "word": " and", "probability": 0.94140625}, {"start": 2204.34, "end": 2204.8, "word": " Q1.", "probability": 0.99658203125}, {"start": 2204.92, "end": 2205.06, "word": " I", "probability": 0.97314453125}, {"start": 2205.06, "end": 2205.2, "word": " mean", "probability": 0.95947265625}, {"start": 2205.2, "end": 2205.32, "word": " the", "probability": 0.68310546875}, {"start": 2205.32, "end": 2205.84, "word": " difference", "probability": 0.81591796875}, {"start": 2205.84, "end": 2206.8, "word": " between", "probability": 0.88134765625}, {"start": 2206.8, "end": 2207.26, "word": " Q3", "probability": 0.981201171875}, {"start": 2207.26, "end": 2207.4, "word": " and", "probability": 0.94580078125}, {"start": 2207.4, "end": 2207.78, "word": " Q1", "probability": 0.994384765625}, {"start": 2207.78, "end": 2208.0, "word": " is", "probability": 0.85107421875}, {"start": 2208.0, "end": 2208.32, "word": " called", "probability": 0.88232421875}, {"start": 2208.32, "end": 2209.42, "word": " the", "probability": 0.873046875}, {"start": 2209.42, "end": 2209.7, "word": " inter", "probability": 0.81689453125}, {"start": 2209.7, "end": 2210.16, "word": "-quartile", "probability": 0.9407958984375}, {"start": 2210.16, "end": 2210.56, "word": " range.", "probability": 0.87646484375}, {"start": 2212.0, "end": 2212.56, "word": " And", "probability": 0.91552734375}, {"start": 2212.56, "end": 2213.2, "word": " this", "probability": 0.9404296875}, {"start": 2213.2, "end": 2213.46, "word": " one", "probability": 0.92431640625}, {"start": 2213.46, "end": 2213.86, "word": " measures", "probability": 0.8505859375}, {"start": 2213.86, "end": 2214.22, "word": " the", "probability": 0.89306640625}, {"start": 2214.22, "end": 2214.62, "word": " spread", "probability": 0.880859375}, {"start": 2214.62, "end": 2215.06, "word": " in", "probability": 0.9443359375}, {"start": 2215.06, "end": 2215.2, "word": " the", "probability": 0.92138671875}, {"start": 2215.2, "end": 2215.42, "word": " middle", "probability": 0.9052734375}, {"start": 2215.42, "end": 2215.78, "word": " 50", "probability": 0.94189453125}, {"start": 2215.78, "end": 2216.0, "word": "%", "probability": 0.87158203125}, {"start": 2216.0, "end": 2216.26, "word": " of", "probability": 0.96435546875}, {"start": 2216.26, "end": 2216.4, "word": " the", "probability": 0.92041015625}, {"start": 2216.4, "end": 2216.68, "word": " data.", "probability": 0.921875}, {"start": 2217.68, "end": 2218.18, "word": " Because", "probability": 0.931640625}, {"start": 2218.18, "end": 2218.34, "word": " if", "probability": 0.89599609375}, {"start": 2218.34, "end": 2218.42, "word": " you", "probability": 0.9619140625}, {"start": 2218.42, "end": 2218.74, "word": " imagine", "probability": 0.89697265625}, {"start": 2218.74, "end": 2219.06, "word": " that,", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 82, "seek": 223957, "start": 2222.25, "end": 2239.57, "text": " This is Q1 and Q3. IQR is the distance between these two values. Now imagine that we have just this data, which represents 50%.", "tokens": [639, 307, 1249, 16, 293, 1249, 18, 13, 28921, 49, 307, 264, 4560, 1296, 613, 732, 4190, 13, 823, 3811, 300, 321, 362, 445, 341, 1412, 11, 597, 8855, 2625, 6856], "avg_logprob": -0.10705566662363708, "compression_ratio": 1.1428571428571428, "no_speech_prob": 0.0, "words": [{"start": 2222.25, "end": 2222.59, "word": " This", "probability": 0.75439453125}, {"start": 2222.59, "end": 2222.77, "word": " is", "probability": 0.94091796875}, {"start": 2222.77, "end": 2223.19, "word": " Q1", "probability": 0.90087890625}, {"start": 2223.19, "end": 2224.61, "word": " and", "probability": 0.89892578125}, {"start": 2224.61, "end": 2225.31, "word": " Q3.", "probability": 0.9794921875}, {"start": 2227.21, "end": 2227.97, "word": " IQR", "probability": 0.896240234375}, {"start": 2227.97, "end": 2229.27, "word": " is", "probability": 0.931640625}, {"start": 2229.27, "end": 2229.41, "word": " the", "probability": 0.919921875}, {"start": 2229.41, "end": 2229.89, "word": " distance", "probability": 0.93212890625}, {"start": 2229.89, "end": 2230.25, "word": " between", "probability": 0.8740234375}, {"start": 2230.25, "end": 2230.53, "word": " these", "probability": 0.86279296875}, {"start": 2230.53, "end": 2230.71, "word": " two", "probability": 0.91552734375}, {"start": 2230.71, "end": 2231.15, "word": " values.", "probability": 0.9697265625}, {"start": 2232.33, "end": 2232.71, "word": " Now", "probability": 0.955078125}, {"start": 2232.71, "end": 2233.05, "word": " imagine", "probability": 0.70556640625}, {"start": 2233.05, "end": 2233.37, "word": " that", "probability": 0.92919921875}, {"start": 2233.37, "end": 2233.55, "word": " we", "probability": 0.953125}, {"start": 2233.55, "end": 2233.75, "word": " have", "probability": 0.93603515625}, {"start": 2233.75, "end": 2234.13, "word": " just", "probability": 0.9189453125}, {"start": 2234.13, "end": 2234.49, "word": " this", "probability": 0.94580078125}, {"start": 2234.49, "end": 2234.87, "word": " data,", "probability": 0.9326171875}, {"start": 2236.25, "end": 2236.59, "word": " which", "probability": 0.9482421875}, {"start": 2236.59, "end": 2237.37, "word": " represents", "probability": 0.86474609375}, {"start": 2237.37, "end": 2239.57, "word": " 50%.", "probability": 0.833740234375}], "temperature": 1.0}, {"id": 83, "seek": 226782, "start": 2241.54, "end": 2267.82, "text": " And IQR, the definition is a Q3. So we have just this data, for example. And IQ3 is Q3 minus Q1. It means IQ3 is the maximum minus the minimum of the 50% of the middle data. So it means this is your range, new range. After you've secluded 25% to the left of Q1,", "tokens": [400, 28921, 49, 11, 264, 7123, 307, 257, 1249, 18, 13, 407, 321, 362, 445, 341, 1412, 11, 337, 1365, 13, 400, 28921, 18, 307, 1249, 18, 3175, 1249, 16, 13, 467, 1355, 28921, 18, 307, 264, 6674, 3175, 264, 7285, 295, 264, 2625, 4, 295, 264, 2808, 1412, 13, 407, 309, 1355, 341, 307, 428, 3613, 11, 777, 3613, 13, 2381, 291, 600, 907, 44412, 3552, 4, 281, 264, 1411, 295, 1249, 16, 11], "avg_logprob": -0.13342928141355515, "compression_ratio": 1.497142857142857, "no_speech_prob": 0.0, "words": [{"start": 2241.54, "end": 2241.9, "word": " And", "probability": 0.86865234375}, {"start": 2241.9, "end": 2242.58, "word": " IQR,", "probability": 0.926513671875}, {"start": 2242.66, "end": 2242.72, "word": " the", "probability": 0.9130859375}, {"start": 2242.72, "end": 2243.12, "word": " definition", "probability": 0.93603515625}, {"start": 2243.12, "end": 2243.58, "word": " is", "probability": 0.8818359375}, {"start": 2243.58, "end": 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So in the presence of outliers, it's better to use IQR instead of using the range. So again, median and the range are not affected by outliers.", "tokens": [28921, 49, 797, 307, 257, 3481, 295, 35709, 300, 307, 406, 15269, 420, 8028, 538, 484, 23646, 420, 8084, 4190, 13, 407, 294, 264, 6814, 295, 484, 23646, 11, 309, 311, 1101, 281, 764, 28921, 49, 2602, 295, 1228, 264, 3613, 13, 407, 797, 11, 26779, 293, 264, 3613, 366, 406, 8028, 538, 484, 23646, 13], "avg_logprob": -0.16461074352264404, "compression_ratio": 1.5696202531645569, "no_speech_prob": 0.0, "words": [{"start": 2357.3, "end": 2357.94, "word": " IQR", "probability": 0.78466796875}, {"start": 2357.94, "end": 2358.18, "word": " again", "probability": 0.42578125}, {"start": 2358.18, "end": 2358.36, "word": " is", "probability": 0.87646484375}, {"start": 2358.36, "end": 2358.46, "word": " a", "probability": 0.91650390625}, {"start": 2358.46, "end": 2358.62, "word": " measure", "probability": 0.796875}, {"start": 2358.62, "end": 2358.8, "word": " of", "probability": 0.94384765625}, {"start": 2358.8, "end": 2359.22, "word": " variability", "probability": 0.98291015625}, {"start": 2359.22, "end": 2359.58, "word": " that", "probability": 0.87841796875}, {"start": 2359.58, "end": 2359.8, "word": " is", "probability": 0.912109375}, {"start": 2359.8, "end": 2360.12, "word": " not", "probability": 0.92724609375}, {"start": 2360.12, "end": 2360.7, "word": " influenced", "probability": 0.79248046875}, {"start": 2360.7, "end": 2361.66, "word": " or", "probability": 0.73779296875}, {"start": 2361.66, "end": 2362.08, "word": " affected", "probability": 0.78125}, {"start": 2362.08, "end": 2362.76, "word": " by", "probability": 0.9560546875}, {"start": 2362.76, "end": 2363.2, "word": " outliers", "probability": 0.886962890625}, {"start": 2363.2, "end": 2363.56, "word": " or", "probability": 0.9169921875}, {"start": 2363.56, "end": 2363.9, "word": " extreme", "probability": 0.84521484375}, {"start": 2363.9, "end": 2364.34, "word": " values.", "probability": 0.9677734375}, {"start": 2365.16, "end": 2365.28, "word": " So", "probability": 0.81396484375}, {"start": 2365.28, "end": 2365.4, "word": " in", "probability": 0.73681640625}, {"start": 2365.4, "end": 2365.52, "word": " the", "probability": 0.9140625}, {"start": 2365.52, "end": 2365.8, "word": " presence", "probability": 0.9677734375}, {"start": 2365.8, "end": 2366.02, "word": " of", "probability": 0.96435546875}, {"start": 2366.02, "end": 2366.44, "word": " outliers,", "probability": 0.943115234375}, {"start": 2366.6, "end": 2366.68, "word": " it's", "probability": 0.720458984375}, {"start": 2366.68, "end": 2366.94, "word": " better", "probability": 0.90966796875}, {"start": 2366.94, "end": 2367.14, "word": " to", "probability": 0.9677734375}, {"start": 2367.14, "end": 2368.0, "word": " use", "probability": 0.888671875}, {"start": 2368.0, "end": 2369.2, "word": " IQR", "probability": 0.98095703125}, {"start": 2369.2, "end": 2369.58, "word": " instead", "probability": 0.8173828125}, {"start": 2369.58, "end": 2369.76, "word": " of", "probability": 0.9638671875}, {"start": 2369.76, "end": 2370.2, "word": " using", "probability": 0.93310546875}, {"start": 2370.2, "end": 2371.24, "word": " the", "probability": 0.671875}, {"start": 2371.24, "end": 2371.52, "word": " range.", "probability": 0.86767578125}, {"start": 2373.46, "end": 2374.16, "word": " So", "probability": 0.89794921875}, {"start": 2374.16, "end": 2374.48, "word": " again,", "probability": 0.9287109375}, {"start": 2375.26, "end": 2375.5, "word": " median", "probability": 0.76513671875}, {"start": 2375.5, "end": 2376.34, "word": " and", "probability": 0.9423828125}, {"start": 2376.34, "end": 2376.5, "word": " the", "probability": 0.6494140625}, {"start": 2376.5, "end": 2376.84, "word": " range", "probability": 0.88720703125}, {"start": 2376.84, "end": 2377.98, "word": " are", "probability": 0.9296875}, {"start": 2377.98, "end": 2378.28, "word": " not", "probability": 0.9443359375}, {"start": 2378.28, "end": 2378.82, "word": " affected", "probability": 0.87255859375}, {"start": 2378.82, "end": 2379.14, "word": " by", "probability": 0.97314453125}, {"start": 2379.14, "end": 2379.56, "word": " outliers.", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 88, "seek": 240700, "start": 2380.32, "end": 2407.0, "text": " So in case of the presence of outliers, we have to use these measures, one as measure of central and the other as measure of spread. So measures like Q1, Q3, and IQR that are not influenced by outliers are called resistant measures. Resistance means in case of outliers, they remain in the same position or approximately in the same position.", "tokens": [407, 294, 1389, 295, 264, 6814, 295, 484, 23646, 11, 321, 362, 281, 764, 613, 8000, 11, 472, 382, 3481, 295, 5777, 293, 264, 661, 382, 3481, 295, 3974, 13, 407, 8000, 411, 1249, 16, 11, 1249, 18, 11, 293, 28921, 49, 300, 366, 406, 15269, 538, 484, 23646, 366, 1219, 20383, 8000, 13, 45647, 1355, 294, 1389, 295, 484, 23646, 11, 436, 6222, 294, 264, 912, 2535, 420, 10447, 294, 264, 912, 2535, 13], "avg_logprob": -0.12469161792021048, "compression_ratio": 1.758974358974359, "no_speech_prob": 0.0, "words": [{"start": 2380.32, "end": 2380.66, "word": " So", "probability": 0.8828125}, {"start": 2380.66, "end": 2380.88, "word": " in", "probability": 0.70703125}, {"start": 2380.88, "end": 2381.18, "word": " case", "probability": 0.9052734375}, {"start": 2381.18, "end": 2382.04, "word": " of", "probability": 0.95654296875}, {"start": 2382.04, "end": 2382.18, "word": " the", 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I mean, don't affect Q1, Q3, and consequently IQR, because IQR is just the distance between Q3 and Q1. So to determine the value of IQR, you have first to compute Q1, Q3, then take the difference between these two.", "tokens": [1436, 484, 23646, 500, 380, 3345, 613, 8000, 13, 286, 914, 11, 500, 380, 3345, 1249, 16, 11, 1249, 18, 11, 293, 47259, 28921, 49, 11, 570, 28921, 49, 307, 445, 264, 4560, 1296, 1249, 18, 293, 1249, 16, 13, 407, 281, 6997, 264, 2158, 295, 28921, 49, 11, 291, 362, 700, 281, 14722, 1249, 16, 11, 1249, 18, 11, 550, 747, 264, 2649, 1296, 613, 732, 13], "avg_logprob": -0.1543251759764077, "compression_ratio": 1.5263157894736843, "no_speech_prob": 0.0, "words": [{"start": 2407.69, "end": 2408.11, "word": " Because", "probability": 0.70556640625}, {"start": 2408.11, "end": 2408.79, "word": " outliers", "probability": 0.83203125}, {"start": 2408.79, "end": 2409.87, "word": " don't", "probability": 0.94921875}, {"start": 2409.87, "end": 2410.33, "word": " affect", "probability": 0.8759765625}, {"start": 2410.33, "end": 2410.85, "word": " these", "probability": 0.78857421875}, {"start": 2410.85, "end": 2411.25, "word": " measures.", "probability": 0.59521484375}, {"start": 2411.39, "end": 2411.47, "word": " I", "probability": 0.98095703125}, {"start": 2411.47, "end": 2411.59, "word": " mean,", "probability": 0.9658203125}, {"start": 2411.65, "end": 2411.81, "word": " don't", "probability": 0.93505859375}, {"start": 2411.81, "end": 2412.23, "word": " affect", "probability": 0.923828125}, {"start": 2412.23, "end": 2413.87, "word": " Q1,", "probability": 0.801513671875}, {"start": 2414.83, "end": 2415.33, "word": " Q3,", "probability": 0.902587890625}, {"start": 2415.91, "end": 2416.77, "word": " and", "probability": 0.94091796875}, {"start": 2416.77, "end": 2417.47, "word": " consequently", "probability": 0.79541015625}, {"start": 2417.47, "end": 2418.11, "word": " IQR,", "probability": 0.93017578125}, {"start": 2418.21, "end": 2418.39, "word": " because", "probability": 0.8935546875}, {"start": 2418.39, "end": 2418.89, "word": " IQR", "probability": 0.9873046875}, {"start": 2418.89, "end": 2419.09, "word": " is", "probability": 0.943359375}, {"start": 2419.09, "end": 2419.43, "word": " just", "probability": 0.916015625}, {"start": 2419.43, "end": 2420.13, "word": " the", "probability": 0.90234375}, {"start": 2420.13, "end": 2420.55, "word": " distance", "probability": 0.94287109375}, {"start": 2420.55, "end": 2420.91, "word": " between", "probability": 0.87939453125}, {"start": 2420.91, "end": 2421.41, "word": " Q3", "probability": 0.9853515625}, {"start": 2421.41, "end": 2421.63, "word": " and", "probability": 0.9404296875}, {"start": 2421.63, "end": 2422.07, "word": " Q1.", "probability": 0.94384765625}, {"start": 2422.95, "end": 2423.53, "word": " So", "probability": 0.962890625}, {"start": 2423.53, "end": 2423.99, "word": " to", "probability": 0.68017578125}, {"start": 2423.99, "end": 2424.59, "word": " determine", "probability": 0.91357421875}, {"start": 2424.59, "end": 2424.99, "word": " the", "probability": 0.85009765625}, {"start": 2424.99, "end": 2425.25, "word": " value", "probability": 0.9716796875}, {"start": 2425.25, "end": 2425.49, "word": " of", "probability": 0.71728515625}, {"start": 2425.49, "end": 2426.15, "word": " IQR,", "probability": 0.97998046875}, {"start": 2426.21, "end": 2426.31, "word": " you", "probability": 0.9580078125}, {"start": 2426.31, "end": 2426.55, "word": " have", "probability": 0.919921875}, {"start": 2426.55, "end": 2426.89, "word": " first", "probability": 0.5126953125}, {"start": 2426.89, "end": 2427.03, "word": " to", "probability": 0.60498046875}, {"start": 2427.03, "end": 2427.33, "word": " compute", "probability": 0.9140625}, {"start": 2427.33, "end": 2427.85, "word": " Q1,", "probability": 0.996826171875}, {"start": 2428.87, "end": 2429.43, "word": " Q3,", "probability": 0.9423828125}, {"start": 2429.75, "end": 2430.05, "word": " then", "probability": 0.82080078125}, {"start": 2430.05, "end": 2430.53, "word": " take", "probability": 0.86962890625}, {"start": 2430.53, "end": 2431.05, "word": " the", "probability": 0.9267578125}, {"start": 2431.05, "end": 2432.91, "word": " difference", "probability": 0.73583984375}, {"start": 2432.91, "end": 2433.77, "word": " between", "probability": 0.794921875}, {"start": 2433.77, "end": 2434.05, "word": " these", "probability": 0.8125}, {"start": 2434.05, "end": 2434.21, "word": " two.", "probability": 0.830078125}], "temperature": 1.0}, {"id": 90, "seek": 246217, "start": 2435.38, "end": 2462.18, "text": " So, for example, suppose we have a data, and that data has Q1 equals 30, and Q3 is 55. Suppose for a data set, that data set has Q1 30, Q3 is 57. The IQR, or Inter Equal Hyper Range,", "tokens": [407, 11, 337, 1365, 11, 7297, 321, 362, 257, 1412, 11, 293, 300, 1412, 575, 1249, 16, 6915, 2217, 11, 293, 1249, 18, 307, 12330, 13, 21360, 337, 257, 1412, 992, 11, 300, 1412, 992, 575, 1249, 16, 2217, 11, 1249, 18, 307, 21423, 13, 440, 28921, 49, 11, 420, 5751, 15624, 304, 29592, 33778, 11], "avg_logprob": -0.2605537406185217, "compression_ratio": 1.3863636363636365, "no_speech_prob": 0.0, "words": [{"start": 2435.38, "end": 2435.78, "word": " So,", "probability": 0.7822265625}, {"start": 2436.12, "end": 2436.32, "word": " for", "probability": 0.93408203125}, {"start": 2436.32, "end": 2436.7, "word": " example,", "probability": 0.97314453125}, {"start": 2438.4, "end": 2438.74, "word": " suppose", "probability": 0.869140625}, {"start": 2438.74, "end": 2438.94, "word": " we", "probability": 0.9248046875}, {"start": 2438.94, "end": 2439.06, "word": " have", "probability": 0.9482421875}, {"start": 2439.06, "end": 2439.16, "word": " a", "probability": 0.85009765625}, {"start": 2439.16, "end": 2439.4, "word": " data,", "probability": 0.943359375}, {"start": 2440.28, "end": 2440.62, "word": " and", "probability": 0.93212890625}, {"start": 2440.62, "end": 2440.84, "word": " that", "probability": 0.9384765625}, {"start": 2440.84, "end": 2441.12, "word": " data", "probability": 0.927734375}, {"start": 2441.12, "end": 2441.58, "word": " has", "probability": 0.943359375}, {"start": 2441.58, "end": 2443.88, "word": " Q1", "probability": 0.913818359375}, {"start": 2443.88, "end": 2445.52, "word": " equals", "probability": 0.619140625}, {"start": 2445.52, "end": 2446.12, "word": " 30,", "probability": 0.93359375}, {"start": 2447.02, "end": 2447.86, "word": " and", "probability": 0.94189453125}, {"start": 2447.86, "end": 2448.72, "word": " Q3", "probability": 0.983154296875}, {"start": 2448.72, "end": 2449.04, "word": " is", "probability": 0.90087890625}, {"start": 2449.04, "end": 2449.54, "word": " 55.", "probability": 0.955078125}, {"start": 2449.72, "end": 2450.1, "word": " Suppose", "probability": 0.78515625}, {"start": 2450.1, "end": 2450.44, "word": " for", "probability": 0.888671875}, {"start": 2450.44, "end": 2451.2, "word": " a", "probability": 0.95654296875}, {"start": 2451.2, "end": 2451.4, "word": " data", "probability": 0.496337890625}, {"start": 2451.4, "end": 2451.74, "word": " set,", "probability": 0.95166015625}, {"start": 2452.9, "end": 2453.18, "word": " that", "probability": 0.8896484375}, {"start": 2453.18, "end": 2453.36, "word": " data", "probability": 0.7802734375}, {"start": 2453.36, "end": 2453.54, "word": " set", "probability": 0.8984375}, {"start": 2453.54, "end": 2453.94, "word": " has", "probability": 0.9423828125}, {"start": 2453.94, "end": 2455.0, "word": " Q1", "probability": 0.96630859375}, {"start": 2455.0, "end": 2455.42, "word": " 30,", "probability": 0.5390625}, {"start": 2455.94, "end": 2456.42, "word": " Q3", "probability": 0.902587890625}, {"start": 2456.42, "end": 2456.58, "word": " is", "probability": 0.88818359375}, {"start": 2456.58, "end": 2457.32, "word": " 57.", "probability": 0.94482421875}, {"start": 2458.84, "end": 2459.2, "word": " The", "probability": 0.86865234375}, {"start": 2459.2, "end": 2460.14, "word": " IQR,", "probability": 0.85009765625}, {"start": 2460.8, "end": 2460.8, "word": " or", "probability": 0.8017578125}, {"start": 2460.8, "end": 2461.36, "word": " Inter", "probability": 0.53076171875}, {"start": 2461.36, "end": 2461.62, "word": " Equal", "probability": 0.6173095703125}, {"start": 2461.62, "end": 2461.86, "word": " Hyper", "probability": 0.1107177734375}, {"start": 2461.86, "end": 2462.18, "word": " Range,", "probability": 0.93212890625}], "temperature": 1.0}, {"id": 91, "seek": 249182, "start": 2462.96, "end": 2491.82, "text": " 57 minus 30 is 27. Now what's the range? The range is maximum for the largest value, which is 17 minus 12. That gives 58. Now look at the difference between the two ranges. The inter-quartile range is 27. The range is 58. There is a big difference between these two values because range", "tokens": [21423, 3175, 2217, 307, 7634, 13, 823, 437, 311, 264, 3613, 30, 440, 3613, 307, 6674, 337, 264, 6443, 2158, 11, 597, 307, 3282, 3175, 2272, 13, 663, 2709, 21786, 13, 823, 574, 412, 264, 2649, 1296, 264, 732, 22526, 13, 440, 728, 12, 358, 446, 794, 3613, 307, 7634, 13, 440, 3613, 307, 21786, 13, 821, 307, 257, 955, 2649, 1296, 613, 732, 4190, 570, 3613], "avg_logprob": -0.18589154499418595, "compression_ratio": 1.6494252873563218, "no_speech_prob": 0.0, "words": [{"start": 2462.96, "end": 2463.54, "word": " 57", "probability": 0.78466796875}, {"start": 2463.54, "end": 2463.88, "word": " minus", "probability": 0.96435546875}, {"start": 2463.88, "end": 2464.18, "word": " 30", "probability": 0.5244140625}, {"start": 2464.18, "end": 2464.32, "word": " is", "probability": 0.89990234375}, {"start": 2464.32, "end": 2464.7, "word": " 27.", "probability": 0.97705078125}, {"start": 2466.52, "end": 2467.24, "word": " 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And these values could be outliers. For this reason, the range value is higher or greater than the required range, which is just the distance of the 50% of the middle data. For this reason, it's better to use the range in case of outliers. Make sense?", "tokens": [5946, 787, 322, 16998, 293, 6443, 13, 400, 613, 4190, 727, 312, 484, 23646, 13, 1171, 341, 1778, 11, 264, 3613, 2158, 307, 2946, 420, 5044, 813, 264, 4739, 3613, 11, 597, 307, 445, 264, 4560, 295, 264, 2625, 4, 295, 264, 2808, 1412, 13, 1171, 341, 1778, 11, 309, 311, 1101, 281, 764, 264, 3613, 294, 1389, 295, 484, 23646, 13, 4387, 2020, 30], "avg_logprob": -0.16394412314349954, "compression_ratio": 1.6111111111111112, "no_speech_prob": 0.0, "words": [{"start": 2492.89, "end": 2493.47, "word": " depends", "probability": 0.327392578125}, {"start": 2493.47, "end": 2494.13, "word": " only", "probability": 0.873046875}, {"start": 2494.13, "end": 2494.97, "word": " on", "probability": 0.8955078125}, {"start": 2494.97, "end": 2495.41, "word": " smallest", "probability": 0.8134765625}, {"start": 2495.41, "end": 2495.75, "word": " and", "probability": 0.94482421875}, {"start": 2495.75, "end": 2496.11, "word": " largest.", "probability": 0.8828125}, {"start": 2496.65, 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"end": 2549.42, "text": " Any question? Five-number summary are smallest value, largest value, also first quartile, third quartile, and the median.", "tokens": [2639, 1168, 30, 9436, 12, 41261, 12691, 366, 16998, 2158, 11, 6443, 2158, 11, 611, 700, 20837, 794, 11, 2636, 20837, 794, 11, 293, 264, 26779, 13], "avg_logprob": -0.19126674426453455, "compression_ratio": 1.2708333333333333, "no_speech_prob": 0.0, "words": [{"start": 2523.3, "end": 2523.56, "word": " Any", "probability": 0.82373046875}, {"start": 2523.56, "end": 2523.94, "word": " question?", "probability": 0.56640625}, {"start": 2528.68, "end": 2529.34, "word": " Five", "probability": 0.426025390625}, {"start": 2529.34, "end": 2529.62, "word": "-number", "probability": 0.650634765625}, {"start": 2529.62, "end": 2529.98, "word": " summary", "probability": 0.69580078125}, {"start": 2529.98, "end": 2532.7, "word": " are", "probability": 0.85009765625}, {"start": 2532.7, "end": 2539.32, "word": " smallest", "probability": 0.83154296875}, {"start": 2539.32, "end": 2539.92, "word": " value,", "probability": 0.96630859375}, {"start": 2541.26, "end": 2541.66, "word": " largest", "probability": 0.89306640625}, {"start": 2541.66, "end": 2542.12, "word": " value,", "probability": 0.9736328125}, {"start": 2543.88, "end": 2544.3, "word": " also", "probability": 0.86083984375}, {"start": 2544.3, "end": 2545.24, "word": " first", "probability": 0.75244140625}, {"start": 2545.24, "end": 2545.94, "word": " quartile,", "probability": 0.95361328125}, {"start": 2547.06, "end": 2547.38, "word": " third", "probability": 0.9306640625}, {"start": 2547.38, "end": 2548.12, "word": " quartile,", "probability": 0.987060546875}, {"start": 2548.66, "end": 2549.02, "word": " and", "probability": 0.94140625}, {"start": 2549.02, "end": 2549.18, "word": " the", "probability": 0.8974609375}, {"start": 2549.18, "end": 2549.42, "word": " median.", "probability": 0.92626953125}], "temperature": 1.0}, {"id": 94, "seek": 257723, "start": 2550.15, "end": 2577.23, "text": " These five numbers are called five-number summary, because by using these statistics, smallest, first, median, third quarter, and largest, you can describe the center spread and the shape of the distribution. So by using five-number summary, you can tell something about it.", "tokens": [1981, 1732, 3547, 366, 1219, 1732, 12, 41261, 12691, 11, 570, 538, 1228, 613, 12523, 11, 16998, 11, 700, 11, 26779, 11, 2636, 6555, 11, 293, 6443, 11, 291, 393, 6786, 264, 3056, 3974, 293, 264, 3909, 295, 264, 7316, 13, 407, 538, 1228, 1732, 12, 41261, 12691, 11, 291, 393, 980, 746, 466, 309, 13], "avg_logprob": -0.19654605681436105, "compression_ratio": 1.6272189349112427, "no_speech_prob": 0.0, "words": [{"start": 2550.15, "end": 2550.55, "word": " These", "probability": 0.8017578125}, {"start": 2550.55, "end": 2550.97, "word": " five", "probability": 0.83154296875}, {"start": 2550.97, "end": 2551.51, "word": " numbers", "probability": 0.8974609375}, {"start": 2551.51, "end": 2552.25, "word": " are", "probability": 0.9462890625}, {"start": 2552.25, "end": 2552.69, "word": " called", "probability": 0.89013671875}, {"start": 2552.69, "end": 2553.13, "word": " five", "probability": 0.78076171875}, {"start": 2553.13, "end": 2553.41, "word": "-number", "probability": 0.74609375}, {"start": 2553.41, "end": 2553.73, "word": " summary,", "probability": 0.76904296875}, {"start": 2554.19, "end": 2554.67, "word": " because", "probability": 0.89697265625}, {"start": 2554.67, "end": 2554.99, "word": " by", "probability": 0.93212890625}, {"start": 2554.99, "end": 2555.39, "word": " using", "probability": 0.92822265625}, {"start": 2555.39, "end": 2555.87, "word": " these", "probability": 0.7353515625}, {"start": 2555.87, "end": 2557.71, "word": " statistics,", "probability": 0.86376953125}, {"start": 2558.11, "end": 2558.95, "word": " smallest,", "probability": 0.91455078125}, {"start": 2559.37, "end": 2559.73, "word": " first,", "probability": 0.6884765625}, {"start": 2560.69, "end": 2561.05, "word": " median,", "probability": 0.8916015625}, {"start": 2561.35, "end": 2561.59, "word": " third", "probability": 0.9189453125}, {"start": 2561.59, "end": 2561.91, "word": " quarter,", "probability": 0.666015625}, {"start": 2562.07, "end": 2562.17, "word": " and", "probability": 0.912109375}, {"start": 2562.17, "end": 2562.55, "word": " largest,", "probability": 0.9072265625}, {"start": 2563.01, "end": 2563.25, "word": " you", "probability": 0.9619140625}, {"start": 2563.25, "end": 2563.47, "word": " can", "probability": 0.9462890625}, {"start": 2563.47, "end": 2564.05, "word": " describe", "probability": 0.8544921875}, {"start": 2564.05, "end": 2565.69, "word": " the", "probability": 0.9052734375}, {"start": 2565.69, "end": 2566.01, "word": " center", "probability": 0.82275390625}, {"start": 2566.01, "end": 2568.07, "word": " spread", "probability": 0.5107421875}, {"start": 2568.07, "end": 2569.05, "word": " and", "probability": 0.79736328125}, {"start": 2569.05, "end": 2569.25, "word": " the", "probability": 0.89453125}, {"start": 2569.25, "end": 2569.49, "word": " shape", "probability": 0.90625}, {"start": 2569.49, "end": 2569.63, "word": " of", "probability": 0.9599609375}, {"start": 2569.63, "end": 2569.77, "word": " the", "probability": 0.411865234375}, {"start": 2569.77, "end": 2570.13, "word": " distribution.", "probability": 0.57373046875}, {"start": 2571.65, "end": 2572.19, "word": " So", "probability": 0.9296875}, {"start": 2572.19, "end": 2572.59, "word": " by", "probability": 0.80322265625}, {"start": 2572.59, "end": 2573.07, "word": " using", "probability": 0.93359375}, {"start": 2573.07, "end": 2574.45, "word": " five", "probability": 0.75927734375}, {"start": 2574.45, "end": 2574.73, "word": "-number", "probability": 0.947021484375}, {"start": 2574.73, "end": 2575.05, "word": " summary,", "probability": 0.85986328125}, {"start": 2575.19, "end": 2575.29, "word": " you", "probability": 0.94873046875}, {"start": 2575.29, "end": 2575.57, "word": " can", "probability": 0.935546875}, {"start": 2575.57, "end": 2575.97, "word": " tell", "probability": 0.828125}, {"start": 2575.97, "end": 2576.45, "word": " something", "probability": 0.86083984375}, {"start": 2576.45, "end": 2576.81, "word": " about", "probability": 0.9072265625}, {"start": 2576.81, "end": 2577.23, "word": " it.", "probability": 0.71875}], "temperature": 1.0}, {"id": 95, "seek": 260553, "start": 2578.33, "end": 2605.53, "text": " The center of the data, I mean the value in the middle, because the median is the value in the middle. Spread, because we can talk about the IQR, which is the range, and also the shape of the data. And let's see, let's move to this slide, slide number 50. Let's see how can we construct something called box plot.", "tokens": [440, 3056, 295, 264, 1412, 11, 286, 914, 264, 2158, 294, 264, 2808, 11, 570, 264, 26779, 307, 264, 2158, 294, 264, 2808, 13, 30308, 11, 570, 321, 393, 751, 466, 264, 28921, 49, 11, 597, 307, 264, 3613, 11, 293, 611, 264, 3909, 295, 264, 1412, 13, 400, 718, 311, 536, 11, 718, 311, 1286, 281, 341, 4137, 11, 4137, 1230, 2625, 13, 961, 311, 536, 577, 393, 321, 7690, 746, 1219, 2424, 7542, 13], "avg_logprob": -0.16670049088341848, "compression_ratio": 1.643979057591623, "no_speech_prob": 0.0, "words": [{"start": 2578.33, "end": 2578.55, "word": " The", "probability": 0.75634765625}, {"start": 2578.55, "end": 2578.85, "word": " center", "probability": 0.88232421875}, {"start": 2578.85, "end": 2579.05, "word": " of", "probability": 0.966796875}, {"start": 2579.05, "end": 2579.15, "word": " the", "probability": 0.916015625}, {"start": 2579.15, "end": 2579.45, "word": " data,", "probability": 0.94482421875}, {"start": 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Box plot can be constructed by using the five number summary. We have smallest value. On the other hand, we have the largest value. Also, we have Q1, the first quartile, the median, and Q3. For symmetric distribution, I mean if the data is bell-shaped. In this case, the vertical line in the box", "tokens": [15112, 7542, 13, 15112, 7542, 393, 312, 17083, 538, 1228, 264, 1732, 1230, 12691, 13, 492, 362, 16998, 2158, 13, 1282, 264, 661, 1011, 11, 321, 362, 264, 6443, 2158, 13, 2743, 11, 321, 362, 1249, 16, 11, 264, 700, 20837, 794, 11, 264, 26779, 11, 293, 1249, 18, 13, 1171, 32330, 7316, 11, 286, 914, 498, 264, 1412, 307, 4549, 12, 23103, 13, 682, 341, 1389, 11, 264, 9429, 1622, 294, 264, 2424], "avg_logprob": -0.170625003973643, "compression_ratio": 1.5148514851485149, "no_speech_prob": 0.0, "words": [{"start": 2607.11, "end": 2607.73, "word": " Box", "probability": 0.52685546875}, {"start": 2607.73, "end": 2608.35, "word": " plot.", "probability": 0.343017578125}, {"start": 2609.83, "end": 2610.45, "word": " Box", "probability": 0.919921875}, {"start": 2610.45, "end": 2610.67, "word": " plot", "probability": 0.95751953125}, {"start": 2610.67, "end": 2610.83, "word": " can", "probability": 0.93505859375}, {"start": 2610.83, "end": 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Look carefully at this vertical line. 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So that means by using box plot, you can tell something about the shape of the distribution. So again, if the data are symmetric around the median,", "tokens": [400, 611, 341, 9429, 1622, 37741, 264, 1412, 666, 732, 38490, 11, 490, 264, 16998, 281, 6443, 11, 570, 456, 366, 2625, 4, 295, 264, 18163, 4544, 2507, 11, 293, 2625, 4, 9134, 3673, 13, 407, 300, 1355, 538, 1228, 2424, 7542, 11, 291, 393, 980, 746, 466, 264, 3909, 295, 264, 7316, 13, 407, 797, 11, 498, 264, 1412, 366, 32330, 926, 264, 26779, 11], "avg_logprob": -0.18178637970739336, "compression_ratio": 1.5219512195121951, "no_speech_prob": 0.0, "words": [{"start": 2657.24, "end": 2657.54, "word": " And", "probability": 0.80419921875}, {"start": 2657.54, "end": 2657.86, "word": " also", "probability": 0.82080078125}, {"start": 2657.86, "end": 2658.26, "word": " this", "probability": 0.70068359375}, {"start": 2658.26, "end": 2658.88, "word": " vertical", "probability": 0.91943359375}, {"start": 2658.88, "end": 2659.32, "word": " line", "probability": 0.9111328125}, {"start": 2659.32, "end": 2659.96, "word": " splits", 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I mean, this vertical line is centered between these two endpoints.", "tokens": [400, 264, 5777, 1622, 11, 341, 2424, 11, 293, 5777, 1622, 366, 18988, 1296, 264, 917, 20552, 13, 286, 914, 11, 341, 9429, 1622, 307, 18988, 1296, 613, 732, 917, 20552, 13], "avg_logprob": -0.16015625, "compression_ratio": 1.6105263157894736, "no_speech_prob": 0.0, "words": [{"start": 2687.33, "end": 2687.73, "word": " And", "probability": 0.84912109375}, {"start": 2687.73, "end": 2687.97, "word": " the", "probability": 0.70654296875}, {"start": 2687.97, "end": 2688.27, "word": " central", "probability": 0.92333984375}, {"start": 2688.27, "end": 2688.73, "word": " line,", "probability": 0.9306640625}, {"start": 2689.09, "end": 2689.35, "word": " this", "probability": 0.93115234375}, {"start": 2689.35, "end": 2689.79, "word": " box,", "probability": 0.93994140625}, {"start": 2690.61, "end": 2690.69, "word": " and", "probability": 0.93017578125}, {"start": 2690.69, "end": 2691.11, "word": " central", "probability": 0.9013671875}, {"start": 2691.11, "end": 2691.61, "word": " line", "probability": 0.93310546875}, {"start": 2691.61, "end": 2693.13, "word": " are", "probability": 0.7802734375}, {"start": 2693.13, "end": 2693.91, "word": " centered", "probability": 0.8759765625}, {"start": 2693.91, "end": 2694.35, "word": " between", "probability": 0.880859375}, {"start": 2694.35, "end": 2694.55, "word": " the", "probability": 0.9091796875}, {"start": 2694.55, "end": 2695.05, "word": " endpoints.", "probability": 0.75146484375}, {"start": 2695.53, "end": 2695.65, "word": " I", "probability": 0.96826171875}, {"start": 2695.65, "end": 2695.89, "word": " mean,", "probability": 0.9658203125}, {"start": 2696.71, "end": 2696.91, "word": " this", "probability": 0.9375}, {"start": 2696.91, "end": 2697.25, "word": " vertical", "probability": 0.6123046875}, {"start": 2697.25, "end": 2697.55, "word": " line", "probability": 0.91064453125}, {"start": 2697.55, "end": 2697.95, "word": " is", "probability": 0.79296875}, {"start": 2697.95, "end": 2698.31, "word": " centered", "probability": 0.87939453125}, {"start": 2698.31, "end": 2698.75, "word": " between", "probability": 0.8720703125}, {"start": 2698.75, "end": 2699.03, "word": " these", "probability": 0.86328125}, {"start": 2699.03, "end": 2699.21, "word": " two", "probability": 0.93212890625}, {"start": 2699.21, "end": 2699.73, "word": " endpoints.", "probability": 0.880126953125}], "temperature": 1.0}, {"id": 100, "seek": 272678, "start": 2700.42, "end": 2726.78, "text": " between Q1 and Q3. And the whole box plot is centered between the smallest and the largest value. And also the distance between the median and the smallest is roughly equal to the distance between the median and the largest. So you can tell something about the shape of the distribution by using the box plot.", "tokens": [1296, 1249, 16, 293, 1249, 18, 13, 400, 264, 1379, 2424, 7542, 307, 18988, 1296, 264, 16998, 293, 264, 6443, 2158, 13, 400, 611, 264, 4560, 1296, 264, 26779, 293, 264, 16998, 307, 9810, 2681, 281, 264, 4560, 1296, 264, 26779, 293, 264, 6443, 13, 407, 291, 393, 980, 746, 466, 264, 3909, 295, 264, 7316, 538, 1228, 264, 2424, 7542, 13], "avg_logprob": -0.20052082907585872, "compression_ratio": 1.834319526627219, "no_speech_prob": 0.0, "words": [{"start": 2700.42, "end": 2700.72, "word": " between", "probability": 0.47412109375}, {"start": 2700.72, "end": 2701.12, "word": " Q1", "probability": 0.83544921875}, {"start": 2701.12, "end": 2701.26, "word": " and", "probability": 0.81396484375}, {"start": 2701.26, "end": 2701.74, "word": " Q3.", "probability": 0.99609375}, {"start": 2702.22, "end": 2702.78, "word": " And", "probability": 0.89111328125}, {"start": 2702.78, "end": 2702.94, "word": " 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Here median and median are the same. The box plot, we have here the median in the middle of the box, also in the middle of the entire data. So you can say that the distribution of this data is symmetric or is bell-shaped. It's normal distribution. On the other hand, if you look here, you will see that the median", "tokens": [440, 4295, 294, 264, 2808, 13, 1692, 26779, 293, 26779, 366, 264, 912, 13, 440, 2424, 7542, 11, 321, 362, 510, 264, 26779, 294, 264, 2808, 295, 264, 2424, 11, 611, 294, 264, 2808, 295, 264, 2302, 1412, 13, 407, 291, 393, 584, 300, 264, 7316, 295, 341, 1412, 307, 32330, 420, 307, 4549, 12, 23103, 13, 467, 311, 2710, 7316, 13, 1282, 264, 661, 1011, 11, 498, 291, 574, 510, 11, 291, 486, 536, 300, 264, 26779], "avg_logprob": -0.19471914292890816, "compression_ratio": 1.765625, "no_speech_prob": 0.0, "words": [{"start": 2732.87, "end": 2733.07, "word": " The", "probability": 0.22216796875}, {"start": 2733.07, "end": 2733.31, "word": " graph", "probability": 0.90576171875}, {"start": 2733.31, "end": 2733.51, "word": " in", "probability": 0.8935546875}, {"start": 2733.51, "end": 2733.69, "word": " the", "probability": 0.923828125}, {"start": 2733.69, "end": 2733.99, "word": " middle.", "probability": 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"probability": 0.90283203125}, {"start": 2760.11, "end": 2760.41, "word": " median", "probability": 0.9765625}], "temperature": 1.0}, {"id": 102, "seek": 278306, "start": 2761.76, "end": 2783.06, "text": " is not in the center of the box. It's near Q3. So the left tail, I mean, the distance between the median and the smallest, this tail is longer than the right tail. In this case, it's called left skewed or skewed to the left.", "tokens": [307, 406, 294, 264, 3056, 295, 264, 2424, 13, 467, 311, 2651, 1249, 18, 13, 407, 264, 1411, 6838, 11, 286, 914, 11, 264, 4560, 1296, 264, 26779, 293, 264, 16998, 11, 341, 6838, 307, 2854, 813, 264, 558, 6838, 13, 682, 341, 1389, 11, 309, 311, 1219, 1411, 8756, 26896, 420, 8756, 26896, 281, 264, 1411, 13], "avg_logprob": -0.14512711409795082, "compression_ratio": 1.5517241379310345, "no_speech_prob": 0.0, "words": [{"start": 2761.76, "end": 2762.02, "word": " is", "probability": 0.40234375}, {"start": 2762.02, "end": 2762.2, "word": " not", "probability": 0.94970703125}, {"start": 2762.2, "end": 2762.36, "word": " in", "probability": 0.92138671875}, {"start": 2762.36, "end": 2762.5, "word": " the", "probability": 0.92138671875}, {"start": 2762.5, "end": 2762.78, "word": " center", "probability": 0.8916015625}, {"start": 2762.78, "end": 2763.08, "word": " of", "probability": 0.96826171875}, {"start": 2763.08, "end": 2763.2, "word": " the", "probability": 0.92529296875}, {"start": 2763.2, "end": 2763.5, "word": " box.", "probability": 0.94921875}, {"start": 2765.26, "end": 2765.86, "word": " It's", "probability": 0.964599609375}, {"start": 2765.86, "end": 2766.16, "word": " near", "probability": 0.8271484375}, {"start": 2766.16, "end": 2766.72, "word": " Q3.", "probability": 0.849609375}, {"start": 2767.92, "end": 2768.28, "word": " So", "probability": 0.92431640625}, {"start": 2768.28, "end": 2768.68, "word": " the", "probability": 0.60009765625}, {"start": 2768.68, "end": 2768.98, "word": " left", "probability": 0.734375}, {"start": 2768.98, "end": 2769.52, "word": " tail,", "probability": 0.86572265625}, {"start": 2770.7, "end": 2770.9, "word": " I", "probability": 0.9423828125}, {"start": 2770.9, "end": 2771.12, "word": " mean,", "probability": 0.9677734375}, {"start": 2771.5, "end": 2771.6, "word": " the", "probability": 0.91064453125}, {"start": 2771.6, "end": 2772.02, "word": " distance", "probability": 0.9365234375}, {"start": 2772.02, "end": 2772.58, "word": " between", "probability": 0.865234375}, {"start": 2772.58, "end": 2772.88, "word": " the", "probability": 0.9228515625}, {"start": 2772.88, "end": 2773.16, "word": " median", "probability": 0.8349609375}, {"start": 2773.16, "end": 2773.44, "word": " and", "probability": 0.9345703125}, {"start": 2773.44, "end": 2773.6, "word": " the", "probability": 0.8818359375}, {"start": 2773.6, "end": 2773.98, "word": " smallest,", "probability": 0.93505859375}, {"start": 2774.74, "end": 2775.14, "word": " this", "probability": 0.9453125}, {"start": 2775.14, "end": 2775.5, "word": " tail", "probability": 0.85791015625}, {"start": 2775.5, "end": 2776.24, "word": " is", "probability": 0.87939453125}, {"start": 2776.24, "end": 2776.62, "word": " longer", "probability": 0.935546875}, {"start": 2776.62, "end": 2776.94, "word": " than", "probability": 0.9443359375}, {"start": 2776.94, "end": 2777.14, "word": " the", "probability": 0.90087890625}, {"start": 2777.14, "end": 2777.32, "word": " right", "probability": 0.927734375}, {"start": 2777.32, "end": 2777.66, "word": " tail.", "probability": 0.8583984375}, {"start": 2779.22, "end": 2779.5, "word": " In", "probability": 0.84619140625}, {"start": 2779.5, "end": 2779.7, "word": " this", "probability": 0.9453125}, {"start": 2779.7, "end": 2780.0, "word": " case,", "probability": 0.9130859375}, {"start": 2780.08, "end": 2780.2, "word": " it's", "probability": 0.962158203125}, {"start": 2780.2, "end": 2780.6, "word": " called", "probability": 0.89306640625}, {"start": 2780.6, "end": 2781.5, "word": " left", "probability": 0.78662109375}, {"start": 2781.5, "end": 2782.08, "word": " skewed", "probability": 0.934814453125}, {"start": 2782.08, "end": 2782.3, "word": " or", "probability": 0.638671875}, {"start": 2782.3, "end": 2782.62, "word": " skewed", "probability": 0.95263671875}, {"start": 2782.62, "end": 2782.76, "word": " to", "probability": 0.95166015625}, {"start": 2782.76, "end": 2782.88, "word": " the", "probability": 0.92138671875}, {"start": 2782.88, "end": 2783.06, "word": " left.", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 103, "seek": 281371, "start": 2784.17, "end": 2813.71, "text": " or negative skewness. So if the data is not symmetric, it might be left skewed. I mean, the left tail is longer than the right tail. On the other hand, if the median is located near Q1, it means the right tail is longer than the left tail, and it's called positive skewed or right skewed.", "tokens": [420, 3671, 8756, 895, 442, 13, 407, 498, 264, 1412, 307, 406, 32330, 11, 309, 1062, 312, 1411, 8756, 26896, 13, 286, 914, 11, 264, 1411, 6838, 307, 2854, 813, 264, 558, 6838, 13, 1282, 264, 661, 1011, 11, 498, 264, 26779, 307, 6870, 2651, 1249, 16, 11, 309, 1355, 264, 558, 6838, 307, 2854, 813, 264, 1411, 6838, 11, 293, 309, 311, 1219, 3353, 8756, 26896, 420, 558, 8756, 26896, 13], "avg_logprob": -0.11386986219719665, "compression_ratio": 1.7202380952380953, "no_speech_prob": 0.0, "words": [{"start": 2784.17, "end": 2784.49, "word": " or", "probability": 0.36328125}, {"start": 2784.49, "end": 2784.85, "word": " negative", "probability": 0.921875}, {"start": 2784.85, "end": 2785.57, "word": " skewness.", "probability": 0.9739583333333334}, {"start": 2786.09, "end": 2786.69, "word": " So", "probability": 0.94384765625}, 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"word": " other", "probability": 0.8837890625}, {"start": 2798.73, "end": 2799.11, "word": " hand,", "probability": 0.90673828125}, {"start": 2800.35, "end": 2800.59, "word": " if", "probability": 0.94873046875}, {"start": 2800.59, "end": 2800.77, "word": " the", "probability": 0.92041015625}, {"start": 2800.77, "end": 2801.13, "word": " median", "probability": 0.94775390625}, {"start": 2801.13, "end": 2802.63, "word": " is", "probability": 0.9453125}, {"start": 2802.63, "end": 2803.23, "word": " located", "probability": 0.955078125}, {"start": 2803.23, "end": 2803.63, "word": " near", "probability": 0.912109375}, {"start": 2803.63, "end": 2804.09, "word": " Q1,", "probability": 0.91796875}, {"start": 2804.91, "end": 2805.19, "word": " it", "probability": 0.94140625}, {"start": 2805.19, "end": 2805.45, "word": " means", "probability": 0.923828125}, {"start": 2805.45, "end": 2805.67, "word": " the", "probability": 0.888671875}, {"start": 2805.67, "end": 2805.95, "word": " right", 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So center is the value in the middle, Q2 or the median. Spread is the distance between Q1 and Q3. So Q3 minus Q1 gives IQR. And finally, you can tell something about the shape of the distribution by just looking at the scatter plot. 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And let's see how can we construct the MaxPlot. In order to construct MaxPlot, you have to compute minimum first or smallest value, largest value. 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Smallest is 0, largest is 1 7. Now, be careful here, 1 7 seems to be an outlier. But so far, we don't explain how can we decide if a data value is considered to be an outlier. But at least 1 7.", "tokens": [1171, 341, 2199, 1365, 11, 1249, 16, 307, 568, 11, 1249, 18, 307, 1025, 11, 293, 264, 26779, 307, 805, 13, 15287, 377, 307, 1958, 11, 6443, 307, 502, 1614, 13, 823, 11, 312, 5026, 510, 11, 502, 1614, 2544, 281, 312, 364, 484, 2753, 13, 583, 370, 1400, 11, 321, 500, 380, 2903, 577, 393, 321, 4536, 498, 257, 1412, 2158, 307, 4888, 281, 312, 364, 484, 2753, 13, 583, 412, 1935, 502, 1614, 13], "avg_logprob": -0.1943993444566603, "compression_ratio": 1.4913294797687862, "no_speech_prob": 0.0, "words": [{"start": 2900.41, "end": 2900.77, "word": " For", "probability": 0.82177734375}, {"start": 2900.77, "end": 2901.11, "word": " this", "probability": 0.943359375}, {"start": 2901.11, "end": 2901.63, "word": " simple", "probability": 0.91259765625}, {"start": 2901.63, "end": 2902.23, "word": " example,", "probability": 0.97314453125}, {"start": 2902.75, "end": 2903.77, "word": " Q1", "probability": 0.62353515625}, {"start": 2903.77, "end": 2903.97, "word": " is", 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Sometimes you are 95% sure that that point is an outlier, but you cannot tell, because you have to have a specific rule that can decide if that point is an outlier or not. But at least it makes sense that that point is considered maybe an outlier. 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Again, as we mentioned, the minimum value is zero. The maximum is 27. The Q1 is 2. The median is 3. The Q3 is 5. Now, if you look at the distance between, does this vertical line lie between the line in the middle or the center of the box? It's not exactly. 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You will see that the right tail is much longer than the left tail because it starts from 3 up to 27.", "tokens": [293, 264, 4914, 295, 341, 365, 3104, 281, 264, 7285, 293, 264, 6674, 13, 509, 486, 536, 300, 264, 558, 6838, 307, 709, 2854, 813, 264, 1411, 6838, 570, 309, 3719, 490, 805, 493, 281, 7634, 13], "avg_logprob": -0.15224095433950424, "compression_ratio": 1.3983739837398375, "no_speech_prob": 0.0, "words": [{"start": 2984.34, "end": 2984.68, "word": " and", "probability": 0.42236328125}, {"start": 2984.68, "end": 2984.88, "word": " the", "probability": 0.884765625}, {"start": 2984.88, "end": 2985.26, "word": " location", "probability": 0.9521484375}, {"start": 2985.26, "end": 2985.46, "word": " of", "probability": 0.96142578125}, {"start": 2985.46, "end": 2985.8, "word": " this", "probability": 0.93310546875}, {"start": 2985.8, "end": 2987.78, "word": " with", "probability": 0.79638671875}, {"start": 2987.78, "end": 2988.4, "word": " respect", "probability": 0.927734375}, {"start": 2988.4, "end": 2988.78, "word": " to", "probability": 0.96875}, {"start": 2988.78, "end": 2989.24, "word": " the", "probability": 0.91357421875}, {"start": 2989.24, "end": 2989.46, "word": " minimum", "probability": 0.96826171875}, {"start": 2989.46, "end": 2990.46, "word": " and", "probability": 0.93359375}, {"start": 2990.46, "end": 2990.6, "word": " the", "probability": 0.84521484375}, {"start": 2990.6, "end": 2991.04, "word": " maximum.", "probability": 0.93505859375}, {"start": 2992.28, "end": 2992.34, "word": " You", "probability": 0.6591796875}, {"start": 2992.34, "end": 2992.48, "word": " will", "probability": 0.7392578125}, {"start": 2992.48, "end": 2992.62, "word": " see", "probability": 0.92626953125}, {"start": 2992.62, "end": 2992.9, "word": " that", "probability": 0.92236328125}, {"start": 2992.9, "end": 2993.96, "word": " the", "probability": 0.8984375}, {"start": 2993.96, "end": 2994.6, "word": " right", "probability": 0.9326171875}, {"start": 2994.6, "end": 2995.08, "word": " tail", "probability": 0.89892578125}, {"start": 2995.08, "end": 2996.22, "word": " is", "probability": 0.94384765625}, {"start": 2996.22, "end": 2996.64, "word": " much", "probability": 0.90869140625}, {"start": 2996.64, "end": 2997.12, "word": " longer", "probability": 0.93994140625}, {"start": 2997.12, "end": 2998.0, "word": " than", "probability": 0.93994140625}, {"start": 2998.0, "end": 2998.22, "word": " the", "probability": 0.91552734375}, {"start": 2998.22, "end": 2998.46, "word": " left", "probability": 0.94091796875}, {"start": 2998.46, "end": 2998.76, "word": " tail", "probability": 0.87646484375}, {"start": 2998.76, "end": 2999.78, "word": " because", "probability": 0.52734375}, {"start": 2999.78, "end": 3000.5, "word": " it", "probability": 0.9521484375}, {"start": 3000.5, "end": 3000.98, "word": " starts", "probability": 0.84375}, {"start": 3000.98, "end": 3001.24, "word": " from", "probability": 0.8955078125}, {"start": 3001.24, "end": 3001.56, "word": " 3", "probability": 0.5341796875}, {"start": 3001.56, "end": 3001.88, "word": " up", "probability": 0.95556640625}, {"start": 3001.88, "end": 3002.04, "word": " to", "probability": 0.96728515625}, {"start": 3002.04, "end": 3002.62, "word": " 27.", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 111, "seek": 303280, "start": 3003.88, "end": 3032.8, "text": " And the other one, from zero to three, is a big distance between three and 27, compared to the other one, zero to three. So it seems to be this is quite skewed, so it's not at all symmetric, because of this value. So maybe by using MaxPlot, you can tell that point is suspected to be an outlier. It has a very long right tail.", "tokens": [400, 264, 661, 472, 11, 490, 4018, 281, 1045, 11, 307, 257, 955, 4560, 1296, 1045, 293, 7634, 11, 5347, 281, 264, 661, 472, 11, 4018, 281, 1045, 13, 407, 309, 2544, 281, 312, 341, 307, 1596, 8756, 26896, 11, 370, 309, 311, 406, 412, 439, 32330, 11, 570, 295, 341, 2158, 13, 407, 1310, 538, 1228, 7402, 33710, 310, 11, 291, 393, 980, 300, 935, 307, 26439, 281, 312, 364, 484, 2753, 13, 467, 575, 257, 588, 938, 558, 6838, 13], "avg_logprob": -0.21743223501975278, "compression_ratio": 1.5352112676056338, "no_speech_prob": 0.0, "words": [{"start": 3003.88, "end": 3004.16, "word": " And", "probability": 0.7509765625}, {"start": 3004.16, "end": 3004.3, "word": " the", "probability": 0.81787109375}, {"start": 3004.3, "end": 3004.52, "word": " other", "probability": 0.88525390625}, {"start": 3004.52, "end": 3004.88, "word": " one,", "probability": 0.91455078125}, {"start": 3005.14, "end": 3005.36, "word": " from", "probability": 0.880859375}, {"start": 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"temperature": 1.0}, {"id": 112, "seek": 305900, "start": 3035.56, "end": 3059.0, "text": " So let's see how can we determine if a point is an outlier or not. Sometimes we can use box plot to determine if the point is an outlier or not. The rule is that a value is considered an outlier", "tokens": [407, 718, 311, 536, 577, 393, 321, 6997, 498, 257, 935, 307, 364, 484, 2753, 420, 406, 13, 4803, 321, 393, 764, 2424, 7542, 281, 6997, 498, 264, 935, 307, 364, 484, 2753, 420, 406, 13, 440, 4978, 307, 300, 257, 2158, 307, 4888, 364, 484, 2753], "avg_logprob": -0.15608723647892475, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 3035.56, "end": 3035.82, "word": " So", "probability": 0.708984375}, {"start": 3035.82, "end": 3036.08, "word": " let's", "probability": 0.82861328125}, {"start": 3036.08, "end": 3036.34, "word": " see", "probability": 0.90576171875}, {"start": 3036.34, "end": 3036.78, "word": " how", "probability": 0.82666015625}, {"start": 3036.78, "end": 3037.1, "word": " can", "probability": 0.642578125}, {"start": 3037.1, "end": 3037.36, "word": " we", "probability": 0.955078125}, {"start": 3037.36, "end": 3038.6, "word": " determine", "probability": 0.908203125}, {"start": 3038.6, "end": 3039.66, "word": " if", "probability": 0.9306640625}, {"start": 3039.66, "end": 3039.82, "word": " a", "probability": 0.97705078125}, {"start": 3039.82, "end": 3040.22, "word": " point", "probability": 0.974609375}, {"start": 3040.22, "end": 3040.96, "word": " is", "probability": 0.95263671875}, {"start": 3040.96, "end": 3041.12, "word": " an", "probability": 0.70166015625}, {"start": 3041.12, "end": 3041.46, "word": " outlier", "probability": 0.6654052734375}, {"start": 3041.46, "end": 3041.62, "word": " or", "probability": 0.90380859375}, {"start": 3041.62, "end": 3041.8, "word": " not.", "probability": 0.95458984375}, {"start": 3044.42, "end": 3045.06, "word": " Sometimes", "probability": 0.8720703125}, {"start": 3045.06, "end": 3045.3, "word": " we", "probability": 0.8095703125}, {"start": 3045.3, "end": 3045.64, "word": " can", "probability": 0.93994140625}, {"start": 3045.64, "end": 3046.32, "word": " use", "probability": 0.875}, {"start": 3046.32, "end": 3047.64, "word": " box", "probability": 0.681640625}, {"start": 3047.64, "end": 3048.04, "word": " plot", "probability": 0.6064453125}, {"start": 3048.04, "end": 3050.4, "word": " to", "probability": 0.87353515625}, {"start": 3050.4, "end": 3050.9, "word": " determine", "probability": 0.90478515625}, {"start": 3050.9, "end": 3051.16, "word": " if", "probability": 0.93994140625}, {"start": 3051.16, "end": 3051.28, "word": " the", "probability": 0.7958984375}, {"start": 3051.28, "end": 3051.54, "word": " point", "probability": 0.9658203125}, {"start": 3051.54, "end": 3051.74, "word": " is", "probability": 0.953125}, {"start": 3051.74, "end": 3051.86, "word": " an", "probability": 0.94580078125}, {"start": 3051.86, "end": 3052.2, "word": " outlier", "probability": 0.95458984375}, {"start": 3052.2, "end": 3052.38, "word": " or", "probability": 0.9287109375}, {"start": 3052.38, "end": 3052.62, "word": " not.", "probability": 0.95068359375}, {"start": 3053.58, "end": 3053.84, "word": " The", "probability": 0.86572265625}, {"start": 3053.84, "end": 3054.1, "word": " rule", "probability": 0.91748046875}, {"start": 3054.1, "end": 3054.62, "word": " is", "probability": 0.94775390625}, {"start": 3054.62, "end": 3054.9, "word": " that", "probability": 0.8583984375}, {"start": 3054.9, "end": 3057.28, "word": " a", "probability": 0.8466796875}, {"start": 3057.28, "end": 3057.62, "word": " value", "probability": 0.97412109375}, {"start": 3057.62, "end": 3057.84, "word": " is", "probability": 0.93798828125}, {"start": 3057.84, "end": 3058.34, "word": " considered", "probability": 0.78271484375}, {"start": 3058.34, "end": 3058.58, "word": " an", "probability": 0.93994140625}, {"start": 3058.58, "end": 3059.0, "word": " outlier", "probability": 0.95751953125}], "temperature": 1.0}, {"id": 113, "seek": 308910, "start": 3060.72, "end": 3089.1, "text": " It is more than 1.5 times the entire quartile range below Q1 or above it. Let's explain the meaning of this sentence. First, let's compute something called lower. The lower limit is not the minimum.", "tokens": [467, 307, 544, 813, 502, 13, 20, 1413, 264, 2302, 20837, 794, 3613, 2507, 1249, 16, 420, 3673, 309, 13, 961, 311, 2903, 264, 3620, 295, 341, 8174, 13, 2386, 11, 718, 311, 14722, 746, 1219, 3126, 13, 440, 3126, 4948, 307, 406, 264, 7285, 13], "avg_logprob": -0.19498005319148937, "compression_ratio": 1.3445945945945945, "no_speech_prob": 0.0, "words": [{"start": 3060.72, "end": 3060.86, "word": " It", "probability": 0.447021484375}, {"start": 3060.86, "end": 3061.04, "word": " is", "probability": 0.8359375}, {"start": 3061.04, "end": 3061.32, "word": " more", "probability": 0.9287109375}, {"start": 3061.32, "end": 3061.58, "word": " than", "probability": 0.9423828125}, {"start": 3061.58, "end": 3061.86, "word": " 1", "probability": 0.89453125}, {"start": 3061.86, "end": 3062.56, "word": ".5", "probability": 0.986083984375}, {"start": 3062.56, "end": 3063.16, "word": " times", "probability": 0.82080078125}, {"start": 3063.16, "end": 3063.48, "word": " the", "probability": 0.80615234375}, {"start": 3063.48, "end": 3063.86, "word": " entire", "probability": 0.61376953125}, {"start": 3063.86, "end": 3064.42, "word": " quartile", "probability": 0.8935546875}, {"start": 3064.42, "end": 3064.78, "word": " range", "probability": 0.86865234375}, {"start": 3064.78, "end": 3065.1, "word": " below", "probability": 0.67822265625}, {"start": 3065.1, "end": 3065.7, "word": " Q1", "probability": 0.6715087890625}, {"start": 3065.7, "end": 3066.12, "word": " or", "probability": 0.826171875}, {"start": 3066.12, "end": 3066.54, "word": " above", "probability": 0.94873046875}, {"start": 3066.54, "end": 3066.8, "word": " it.", "probability": 0.4404296875}, {"start": 3068.44, "end": 3069.28, "word": " Let's", "probability": 0.93408203125}, {"start": 3069.28, "end": 3069.7, "word": " explain", "probability": 0.8701171875}, {"start": 3069.7, "end": 3070.06, "word": " the", "probability": 0.92236328125}, {"start": 3070.06, "end": 3070.36, "word": " meaning", "probability": 0.86279296875}, {"start": 3070.36, "end": 3071.42, "word": " of", "probability": 0.9580078125}, {"start": 3071.42, "end": 3071.68, "word": " this", "probability": 0.9365234375}, {"start": 3071.68, "end": 3072.26, "word": " sentence.", "probability": 0.92578125}, {"start": 3075.26, "end": 3076.1, "word": " First,", "probability": 0.90771484375}, {"start": 3076.2, "end": 3076.44, "word": " let's", "probability": 0.973388671875}, {"start": 3076.44, "end": 3076.88, "word": " compute", "probability": 0.9228515625}, {"start": 3076.88, "end": 3078.26, "word": " something", "probability": 0.861328125}, {"start": 3078.26, "end": 3079.46, "word": " called", "probability": 0.87255859375}, {"start": 3079.46, "end": 3080.1, "word": " lower.", "probability": 0.4814453125}, {"start": 3083.74, "end": 3084.58, "word": " The", "probability": 0.59130859375}, {"start": 3084.58, "end": 3084.82, "word": " lower", "probability": 0.85546875}, {"start": 3084.82, "end": 3085.3, "word": " limit", "probability": 0.96533203125}, {"start": 3085.3, "end": 3088.54, "word": " is", "probability": 0.81640625}, {"start": 3088.54, "end": 3088.72, "word": " not", "probability": 0.94384765625}, {"start": 3088.72, "end": 3088.86, "word": " the", "probability": 0.90380859375}, {"start": 3088.86, "end": 3089.1, "word": " minimum.", "probability": 0.974609375}], "temperature": 1.0}, {"id": 114, "seek": 311746, "start": 3090.1, "end": 3117.46, "text": " It's Q1 minus 1.5 IQR. This is the lower limit. So it's 1.5 times IQR below Q1. This is the lower limit. The upper limit, Q3,", "tokens": [467, 311, 1249, 16, 3175, 502, 13, 20, 28921, 49, 13, 639, 307, 264, 3126, 4948, 13, 407, 309, 311, 502, 13, 20, 1413, 28921, 49, 2507, 1249, 16, 13, 639, 307, 264, 3126, 4948, 13, 440, 6597, 4948, 11, 1249, 18, 11], "avg_logprob": -0.1624644896523519, "compression_ratio": 1.3695652173913044, "no_speech_prob": 0.0, "words": [{"start": 3090.1, "end": 3090.98, "word": " It's", "probability": 0.65234375}, {"start": 3090.98, "end": 3091.86, "word": " Q1", "probability": 0.7110595703125}, {"start": 3091.86, "end": 3094.16, "word": " minus", "probability": 0.88232421875}, {"start": 3094.16, "end": 3094.94, "word": " 1", "probability": 0.89208984375}, {"start": 3094.94, "end": 3095.66, "word": ".5", "probability": 0.990234375}, {"start": 3095.66, "end": 3097.78, "word": " IQR.", "probability": 0.7919921875}, {"start": 3098.1, "end": 3098.58, "word": " This", "probability": 0.82763671875}, {"start": 3098.58, "end": 3098.68, "word": " is", "probability": 0.95068359375}, {"start": 3098.68, "end": 3098.82, "word": " the", "probability": 0.9013671875}, {"start": 3098.82, "end": 3099.0, "word": " lower", "probability": 0.796875}, {"start": 3099.0, "end": 3099.28, "word": " limit.", "probability": 0.9189453125}, {"start": 3102.28, "end": 3103.16, "word": " So", "probability": 0.94580078125}, {"start": 3103.16, "end": 3103.54, "word": " it's", "probability": 0.891357421875}, {"start": 3103.54, "end": 3103.96, "word": " 1", "probability": 0.99267578125}, {"start": 3103.96, "end": 3104.6, "word": ".5", "probability": 0.99853515625}, {"start": 3104.6, "end": 3105.12, "word": " times", "probability": 0.8857421875}, {"start": 3105.12, "end": 3105.84, "word": " IQR", "probability": 0.97802734375}, {"start": 3105.84, "end": 3106.22, "word": " below", "probability": 0.87939453125}, {"start": 3106.22, "end": 3106.8, "word": " Q1.", "probability": 0.990966796875}, {"start": 3107.0, "end": 3107.18, "word": " This", "probability": 0.69873046875}, {"start": 3107.18, "end": 3107.26, "word": " is", "probability": 0.9482421875}, {"start": 3107.26, "end": 3107.38, "word": " the", "probability": 0.8798828125}, {"start": 3107.38, "end": 3107.56, "word": " lower", "probability": 0.8935546875}, {"start": 3107.56, "end": 3107.84, "word": " limit.", "probability": 0.96728515625}, {"start": 3109.7, "end": 3109.9, "word": " The", "probability": 0.884765625}, {"start": 3109.9, "end": 3110.16, "word": " upper", "probability": 0.7939453125}, {"start": 3110.16, "end": 3110.62, "word": " limit,", "probability": 0.96923828125}, {"start": 3114.68, "end": 3117.46, "word": " Q3,", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 115, "seek": 314507, "start": 3118.79, "end": 3145.07, "text": " plus 1.5 times IQR. So we computed lower and upper limit by using these rules. Q1 minus 1.5 IQR. So it's 1.5 times IQR below Q1 and 1.5 times IQR above Q1. Now, any value.", "tokens": [1804, 502, 13, 20, 1413, 28921, 49, 13, 407, 321, 40610, 3126, 293, 6597, 4948, 538, 1228, 613, 4474, 13, 1249, 16, 3175, 502, 13, 20, 28921, 49, 13, 407, 309, 311, 502, 13, 20, 1413, 28921, 49, 2507, 1249, 16, 293, 502, 13, 20, 1413, 28921, 49, 3673, 1249, 16, 13, 823, 11, 604, 2158, 13], "avg_logprob": -0.1577316797498999, "compression_ratio": 1.376, "no_speech_prob": 0.0, "words": [{"start": 3118.79, "end": 3119.27, "word": " plus", "probability": 0.2666015625}, {"start": 3119.27, "end": 3119.55, "word": " 1", "probability": 0.93994140625}, {"start": 3119.55, "end": 3120.21, "word": ".5", "probability": 0.97900390625}, {"start": 3120.21, "end": 3120.71, "word": " times", "probability": 0.82861328125}, {"start": 3120.71, "end": 3121.51, "word": " IQR.", "probability": 0.92822265625}, {"start": 3122.65, "end": 3123.61, "word": " So", "probability": 0.9521484375}, {"start": 3123.61, "end": 3123.79, "word": " we", "probability": 0.7021484375}, {"start": 3123.79, "end": 3124.23, "word": " computed", "probability": 0.91796875}, {"start": 3124.23, "end": 3125.53, "word": " lower", "probability": 0.89404296875}, {"start": 3125.53, "end": 3126.61, "word": " and", "probability": 0.9248046875}, {"start": 3126.61, "end": 3126.89, "word": " upper", "probability": 0.8154296875}, {"start": 3126.89, "end": 3127.17, "word": " limit", "probability": 0.9072265625}, {"start": 3127.17, "end": 3127.37, "word": " by", "probability": 0.349853515625}, {"start": 3127.37, "end": 3127.55, "word": " using", "probability": 0.916015625}, {"start": 3127.55, "end": 3127.81, "word": " these", "probability": 0.58837890625}, {"start": 3127.81, "end": 3128.19, "word": " rules.", "probability": 0.57861328125}, {"start": 3129.13, "end": 3129.45, "word": " Q1", "probability": 0.964599609375}, {"start": 3129.45, "end": 3129.75, "word": " minus", "probability": 0.94921875}, {"start": 3129.75, "end": 3129.97, "word": " 1", "probability": 0.99267578125}, {"start": 3129.97, "end": 3130.35, "word": ".5", "probability": 0.99609375}, {"start": 3130.35, "end": 3130.99, "word": " IQR.", "probability": 0.92333984375}, {"start": 3132.39, "end": 3133.35, "word": " So", "probability": 0.9560546875}, {"start": 3133.35, "end": 3133.79, "word": " it's", "probability": 0.931396484375}, {"start": 3133.79, "end": 3134.29, "word": " 1", "probability": 0.98583984375}, {"start": 3134.29, "end": 3134.93, "word": ".5", "probability": 0.998779296875}, {"start": 3134.93, "end": 3135.45, "word": " times", "probability": 0.91259765625}, {"start": 3135.45, "end": 3136.27, "word": " IQR", "probability": 0.984375}, {"start": 3136.27, "end": 3136.67, "word": " below", "probability": 0.8740234375}, {"start": 3136.67, "end": 3137.17, "word": " Q1", "probability": 0.990478515625}, {"start": 3137.17, "end": 3138.69, "word": " and", "probability": 0.462890625}, {"start": 3138.69, "end": 3138.95, "word": " 1", "probability": 0.99365234375}, {"start": 3138.95, "end": 3139.45, "word": ".5", "probability": 0.998779296875}, {"start": 3139.45, "end": 3139.85, "word": " times", "probability": 0.89404296875}, {"start": 3139.85, "end": 3140.51, "word": " IQR", "probability": 0.98193359375}, {"start": 3140.51, "end": 3140.95, "word": " above", "probability": 0.95361328125}, {"start": 3140.95, "end": 3141.57, "word": " Q1.", "probability": 0.8212890625}, {"start": 3143.05, "end": 3143.45, "word": " Now,", "probability": 0.8701171875}, {"start": 3144.39, "end": 3144.71, "word": " any", "probability": 0.87451171875}, {"start": 3144.71, "end": 3145.07, "word": " value.", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 116, "seek": 317945, "start": 3151.15, "end": 3179.45, "text": " Is it smaller than the lower limit or greater than the upper limit? Any value.", "tokens": [1119, 309, 4356, 813, 264, 3126, 4948, 420, 5044, 813, 264, 6597, 4948, 30, 2639, 2158, 13], "avg_logprob": -0.3680555688010322, "compression_ratio": 1.1791044776119404, "no_speech_prob": 0.0, "words": [{"start": 3151.15, "end": 3151.43, "word": " Is", "probability": 0.2724609375}, {"start": 3151.43, "end": 3151.65, "word": " it", "probability": 0.58251953125}, {"start": 3151.65, "end": 3152.19, "word": " smaller", "probability": 0.818359375}, {"start": 3152.19, "end": 3152.53, "word": " than", "probability": 0.9140625}, {"start": 3152.53, "end": 3158.61, "word": " the", "probability": 0.297607421875}, {"start": 3158.61, "end": 3158.87, "word": " lower", "probability": 0.83935546875}, {"start": 3158.87, "end": 3159.51, "word": " limit", "probability": 0.966796875}, {"start": 3159.51, "end": 3165.99, "word": " or", "probability": 0.372314453125}, {"start": 3165.99, "end": 3166.39, "word": " greater", "probability": 0.896484375}, {"start": 3166.39, "end": 3166.79, "word": " than", "probability": 0.9453125}, {"start": 3166.79, "end": 3173.29, "word": " the", "probability": 0.685546875}, {"start": 3173.29, "end": 3173.63, "word": " upper", "probability": 0.85498046875}, {"start": 3173.63, "end": 3174.15, "word": " limit?", "probability": 0.96630859375}, {"start": 3178.33, "end": 3179.11, "word": " Any", "probability": 0.8525390625}, {"start": 3179.11, "end": 3179.45, "word": " value.", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 117, "seek": 320710, "start": 3180.5, "end": 3207.1, "text": " smaller than the lower limit and greater than the upper limit is considered to be an outlier. This is the rule how can you tell if the point or data value is outlier or not. Just compute lower limit and upper limit.", "tokens": [4356, 813, 264, 3126, 4948, 293, 5044, 813, 264, 6597, 4948, 307, 4888, 281, 312, 364, 484, 2753, 13, 639, 307, 264, 4978, 577, 393, 291, 980, 498, 264, 935, 420, 1412, 2158, 307, 484, 2753, 420, 406, 13, 1449, 14722, 3126, 4948, 293, 6597, 4948, 13], "avg_logprob": -0.20556641183793545, "compression_ratio": 1.6119402985074627, "no_speech_prob": 0.0, "words": [{"start": 3180.5, "end": 3181.04, "word": " smaller", "probability": 0.187744140625}, {"start": 3181.04, "end": 3181.42, "word": " than", "probability": 0.931640625}, {"start": 3181.42, "end": 3183.08, "word": " the", "probability": 0.81640625}, {"start": 3183.08, "end": 3183.3, "word": " lower", "probability": 0.84228515625}, {"start": 3183.3, "end": 3183.62, "word": " limit", "probability": 0.94384765625}, {"start": 3183.62, "end": 3184.6, "word": " and", "probability": 0.6484375}, {"start": 3184.6, "end": 3184.92, "word": " greater", "probability": 0.8515625}, {"start": 3184.92, "end": 3185.26, "word": " than", "probability": 0.93701171875}, {"start": 3185.26, "end": 3185.56, "word": " the", "probability": 0.904296875}, {"start": 3185.56, "end": 3186.1, "word": " upper", "probability": 0.861328125}, {"start": 3186.1, "end": 3186.42, "word": " limit", "probability": 0.966796875}, {"start": 3186.42, "end": 3186.72, "word": " is", "probability": 0.599609375}, {"start": 3186.72, "end": 3187.26, "word": " considered", "probability": 0.7880859375}, {"start": 3187.26, "end": 3193.26, "word": " to", "probability": 0.8837890625}, {"start": 3193.26, "end": 3194.98, "word": " be", "probability": 0.955078125}, {"start": 3194.98, "end": 3195.88, "word": " an", "probability": 0.9189453125}, {"start": 3195.88, "end": 3196.42, "word": " outlier.", "probability": 0.799072265625}, {"start": 3198.8, "end": 3199.26, "word": " This", "probability": 0.578125}, {"start": 3199.26, "end": 3199.4, "word": " is", "probability": 0.93017578125}, {"start": 3199.4, "end": 3199.54, "word": " the", "probability": 0.72998046875}, {"start": 3199.54, "end": 3199.76, "word": " rule", "probability": 0.9208984375}, {"start": 3199.76, "end": 3200.04, "word": " how", "probability": 0.30712890625}, {"start": 3200.04, "end": 3200.28, "word": " can", "probability": 0.7197265625}, {"start": 3200.28, "end": 3200.46, "word": " you", "probability": 0.95166015625}, {"start": 3200.46, "end": 3200.72, "word": " tell", "probability": 0.880859375}, {"start": 3200.72, "end": 3201.04, "word": " if", "probability": 0.93359375}, {"start": 3201.04, "end": 3201.18, "word": " the", "probability": 0.82177734375}, {"start": 3201.18, "end": 3201.48, "word": " point", "probability": 0.9609375}, {"start": 3201.48, "end": 3201.98, "word": " or", "probability": 0.92041015625}, {"start": 3201.98, "end": 3202.2, "word": " data", "probability": 0.87255859375}, {"start": 3202.2, "end": 3202.66, "word": " value", "probability": 0.96240234375}, {"start": 3202.66, "end": 3203.64, "word": " is", "probability": 0.9443359375}, {"start": 3203.64, "end": 3204.1, "word": " outlier", "probability": 0.8271484375}, {"start": 3204.1, "end": 3204.28, "word": " or", "probability": 0.9052734375}, {"start": 3204.28, "end": 3204.42, "word": " not.", "probability": 0.9443359375}, {"start": 3204.54, "end": 3204.78, "word": " Just", "probability": 0.85009765625}, {"start": 3204.78, "end": 3205.16, "word": " compute", "probability": 0.89697265625}, {"start": 3205.16, "end": 3205.62, "word": " lower", "probability": 0.771484375}, {"start": 3205.62, "end": 3206.02, "word": " limit", "probability": 0.943359375}, {"start": 3206.02, "end": 3206.38, "word": " and", "probability": 0.939453125}, {"start": 3206.38, "end": 3206.74, "word": " upper", "probability": 0.826171875}, {"start": 3206.74, "end": 3207.1, "word": " limit.", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 118, "seek": 323768, "start": 3209.78, "end": 3237.68, "text": " So lower limit, Q1 minus 1.5IQ3. Upper limit, Q3 plus 1.5. This is a constant. Now let's go back to the previous example, which was, which Q1 was, what's the value of Q1? Q1 was 2. Q3 is 5.", "tokens": [407, 3126, 4948, 11, 1249, 16, 3175, 502, 13, 20, 40, 48, 18, 13, 36926, 4948, 11, 1249, 18, 1804, 502, 13, 20, 13, 639, 307, 257, 5754, 13, 823, 718, 311, 352, 646, 281, 264, 3894, 1365, 11, 597, 390, 11, 597, 1249, 16, 390, 11, 437, 311, 264, 2158, 295, 1249, 16, 30, 1249, 16, 390, 568, 13, 1249, 18, 307, 1025, 13], "avg_logprob": -0.2402935673793157, "compression_ratio": 1.3380281690140845, "no_speech_prob": 0.0, "words": [{"start": 3209.78, "end": 3210.04, "word": " So", "probability": 0.7666015625}, {"start": 3210.04, "end": 3210.28, "word": " lower", "probability": 0.6044921875}, {"start": 3210.28, "end": 3210.6, "word": " limit,", "probability": 0.95068359375}, {"start": 3210.78, "end": 3211.14, "word": " Q1", "probability": 0.86279296875}, {"start": 3211.14, "end": 3211.54, "word": " minus", "probability": 0.8427734375}, {"start": 3211.54, "end": 3211.88, "word": " 1", "probability": 0.96044921875}, {"start": 3211.88, "end": 3213.14, "word": ".5IQ3.", "probability": 0.821044921875}, {"start": 3214.18, "end": 3214.56, "word": " Upper", "probability": 0.8974609375}, {"start": 3214.56, "end": 3214.92, "word": " limit,", "probability": 0.96484375}, {"start": 3215.14, "end": 3215.58, "word": " Q3", "probability": 0.985107421875}, {"start": 3215.58, "end": 3215.92, "word": " plus", "probability": 0.94482421875}, {"start": 3215.92, "end": 3216.24, "word": " 1", "probability": 0.96484375}, {"start": 3216.24, "end": 3217.8, "word": ".5.", "probability": 0.87255859375}, {"start": 3217.94, "end": 3218.22, "word": " This", "probability": 0.60986328125}, {"start": 3218.22, "end": 3218.32, "word": " is", "probability": 0.91015625}, {"start": 3218.32, "end": 3218.4, "word": " a", "probability": 0.284912109375}, {"start": 3218.4, "end": 3218.62, "word": " constant.", "probability": 0.904296875}, {"start": 3223.2, "end": 3223.9, "word": " Now", "probability": 0.94921875}, {"start": 3223.9, "end": 3224.14, "word": " let's", "probability": 0.841552734375}, {"start": 3224.14, "end": 3224.28, "word": " go", "probability": 0.9658203125}, {"start": 3224.28, "end": 3224.52, "word": " back", "probability": 0.87158203125}, {"start": 3224.52, "end": 3224.66, "word": " to", "probability": 0.96533203125}, {"start": 3224.66, "end": 3224.78, "word": " the", "probability": 0.919921875}, {"start": 3224.78, "end": 3224.98, "word": " previous", "probability": 0.80322265625}, {"start": 3224.98, "end": 3225.54, "word": " example,", "probability": 0.9736328125}, {"start": 3226.64, "end": 3227.04, "word": " which", "probability": 0.94921875}, {"start": 3227.04, "end": 3227.44, "word": " was,", "probability": 0.4541015625}, {"start": 3228.22, "end": 3228.58, "word": " which", "probability": 0.912109375}, {"start": 3228.58, "end": 3229.04, "word": " Q1", "probability": 0.989013671875}, {"start": 3229.04, "end": 3229.42, "word": " was,", "probability": 0.9501953125}, {"start": 3229.64, "end": 3229.96, "word": " what's", "probability": 0.756103515625}, {"start": 3229.96, "end": 3230.04, "word": " the", "probability": 0.919921875}, {"start": 3230.04, "end": 3230.16, "word": " value", "probability": 0.98193359375}, {"start": 3230.16, "end": 3230.34, "word": " of", "probability": 0.953125}, {"start": 3230.34, "end": 3230.72, "word": " Q1?", "probability": 0.995849609375}, {"start": 3232.72, "end": 3233.42, "word": " Q1", "probability": 0.990234375}, {"start": 3233.42, "end": 3233.8, "word": " was", "probability": 0.9453125}, {"start": 3233.8, "end": 3234.14, "word": " 2.", "probability": 0.69580078125}, {"start": 3236.42, "end": 3237.12, "word": " Q3", "probability": 0.78369140625}, {"start": 3237.12, "end": 3237.32, "word": " is", "probability": 0.3203125}, {"start": 3237.32, "end": 3237.68, "word": " 5.", "probability": 0.35205078125}], "temperature": 1.0}, {"id": 119, "seek": 326795, "start": 3240.65, "end": 3267.95, "text": " In order to turn an outlier, you don't need the value, the median. Now, Q3 is 5, Q1 is 2, so IQR is 3. That's the value of IQR. Now, lower limit, A times 2 minus 1.5 times IQR3.", "tokens": [682, 1668, 281, 1261, 364, 484, 2753, 11, 291, 500, 380, 643, 264, 2158, 11, 264, 26779, 13, 823, 11, 1249, 18, 307, 1025, 11, 1249, 16, 307, 568, 11, 370, 28921, 49, 307, 805, 13, 663, 311, 264, 2158, 295, 28921, 49, 13, 823, 11, 3126, 4948, 11, 316, 1413, 568, 3175, 502, 13, 20, 1413, 28921, 49, 18, 13], "avg_logprob": -0.3026713656802331, "compression_ratio": 1.3185185185185184, "no_speech_prob": 0.0, "words": [{"start": 3240.6500000000005, "end": 3241.3700000000003, "word": " In", "probability": 0.449462890625}, {"start": 3241.3700000000003, "end": 3242.09, "word": " order", "probability": 0.908203125}, {"start": 3242.09, "end": 3242.33, "word": " to", "probability": 0.96240234375}, {"start": 3242.33, "end": 3242.59, "word": " turn", "probability": 0.591796875}, {"start": 3242.59, "end": 3243.37, "word": " an", "probability": 0.1346435546875}, {"start": 3243.37, "end": 3243.73, "word": " outlier,", "probability": 0.7783203125}, {"start": 3243.93, "end": 3243.95, "word": " you", "probability": 0.93505859375}, {"start": 3243.95, "end": 3244.13, "word": " don't", "probability": 0.967529296875}, {"start": 3244.13, "end": 3244.51, "word": " need", "probability": 0.9267578125}, {"start": 3244.51, "end": 3245.23, "word": " the", "probability": 0.8271484375}, {"start": 3245.23, "end": 3245.49, "word": " value,", "probability": 0.892578125}, {"start": 3245.89, "end": 3246.31, "word": " the", "probability": 0.77392578125}, {"start": 3246.31, "end": 3246.57, "word": " median.", "probability": 0.955078125}, {"start": 3247.11, "end": 3247.65, "word": " Now,", "probability": 0.50048828125}, {"start": 3248.49, "end": 3249.07, "word": " Q3", "probability": 0.66943359375}, {"start": 3249.07, "end": 3249.19, "word": " is", "probability": 0.1859130859375}, {"start": 3249.19, "end": 3249.47, "word": " 5,", "probability": 0.66796875}, {"start": 3249.59, "end": 3249.91, "word": " Q1", "probability": 0.9736328125}, {"start": 3249.91, "end": 3250.07, "word": " is", "probability": 0.9482421875}, {"start": 3250.07, "end": 3250.27, "word": " 2,", "probability": 0.9619140625}, {"start": 3250.37, "end": 3250.49, "word": " so", "probability": 0.9326171875}, {"start": 3250.49, "end": 3251.15, "word": " IQR", "probability": 0.89501953125}, {"start": 3251.15, "end": 3254.13, "word": " is", "probability": 0.80078125}, {"start": 3254.13, "end": 3254.47, "word": " 3.", "probability": 0.87841796875}, {"start": 3255.27, "end": 3255.65, "word": " That's", "probability": 0.814208984375}, {"start": 3255.65, "end": 3255.77, "word": " the", "probability": 0.91650390625}, {"start": 3255.77, "end": 3256.03, "word": " value", "probability": 0.97802734375}, {"start": 3256.03, "end": 3256.41, "word": " of", "probability": 0.962890625}, {"start": 3256.41, "end": 3257.43, "word": " IQR.", "probability": 0.708740234375}, {"start": 3257.63, "end": 3258.13, "word": " Now,", "probability": 0.8974609375}, {"start": 3258.25, "end": 3258.45, "word": " lower", "probability": 0.69189453125}, {"start": 3258.45, "end": 3258.91, "word": " limit,", "probability": 0.9755859375}, {"start": 3260.83, "end": 3261.05, "word": " A", "probability": 0.61376953125}, {"start": 3261.05, "end": 3261.39, "word": " times", "probability": 0.1827392578125}, {"start": 3261.39, "end": 3263.35, "word": " 2", "probability": 0.85107421875}, {"start": 3263.35, "end": 3265.15, "word": " minus", "probability": 0.90576171875}, {"start": 3265.15, "end": 3265.43, "word": " 1", "probability": 0.97705078125}, {"start": 3265.43, "end": 3266.03, "word": ".5", "probability": 0.986328125}, {"start": 3266.03, "end": 3266.53, "word": " times", "probability": 0.904296875}, {"start": 3266.53, "end": 3267.95, "word": " IQR3.", "probability": 0.7833658854166666}], "temperature": 1.0}, {"id": 120, "seek": 329769, "start": 3269.11, "end": 3297.69, "text": " So that's minus 2.5. U3 plus U3 is 3. It's 5, sorry. It's 5 plus 1.5. That gives 9.5. Now, any point or any data value, any data value falls below minus 2.5. I mean smaller than minus 2.5.", "tokens": [407, 300, 311, 3175, 568, 13, 20, 13, 624, 18, 1804, 624, 18, 307, 805, 13, 467, 311, 1025, 11, 2597, 13, 467, 311, 1025, 1804, 502, 13, 20, 13, 663, 2709, 1722, 13, 20, 13, 823, 11, 604, 935, 420, 604, 1412, 2158, 11, 604, 1412, 2158, 8804, 2507, 3175, 568, 13, 20, 13, 286, 914, 4356, 813, 3175, 568, 13, 20, 13], "avg_logprob": -0.18485576923076924, "compression_ratio": 1.4427480916030535, "no_speech_prob": 0.0, "words": [{"start": 3269.11, "end": 3269.37, "word": " So", "probability": 0.166748046875}, {"start": 3269.37, "end": 3269.63, "word": " that's", "probability": 0.920654296875}, {"start": 3269.63, "end": 3270.11, "word": " minus", "probability": 0.9052734375}, {"start": 3270.11, "end": 3271.35, "word": " 2", "probability": 0.93115234375}, {"start": 3271.35, "end": 3271.83, "word": ".5.", "probability": 0.98486328125}, {"start": 3273.55, "end": 3274.31, "word": " U3", "probability": 0.722900390625}, {"start": 3274.31, "end": 3274.81, "word": " plus", "probability": 0.9267578125}, {"start": 3274.81, "end": 3275.75, "word": " U3", "probability": 0.70166015625}, {"start": 3275.75, "end": 3275.91, "word": " is", "probability": 0.84716796875}, {"start": 3275.91, "end": 3276.23, "word": " 3.", "probability": 0.701171875}, {"start": 3276.41, "end": 3276.77, "word": " It's", "probability": 0.830078125}, {"start": 3276.77, "end": 3276.97, "word": " 5,", "probability": 0.9521484375}, {"start": 3277.09, "end": 3277.27, "word": " sorry.", "probability": 0.85888671875}, {"start": 3277.97, "end": 3278.39, "word": " It's", "probability": 0.930908203125}, {"start": 3278.39, "end": 3278.67, "word": " 5", "probability": 0.9833984375}, {"start": 3278.67, "end": 3279.09, "word": " plus", "probability": 0.94189453125}, {"start": 3279.09, "end": 3280.43, "word": " 1", "probability": 0.2197265625}, {"start": 3280.43, "end": 3281.17, "word": ".5.", "probability": 0.949462890625}, {"start": 3281.65, "end": 3282.05, "word": " That", "probability": 0.880859375}, {"start": 3282.05, "end": 3282.41, "word": " gives", "probability": 0.8779296875}, {"start": 3282.41, "end": 3284.25, "word": " 9", "probability": 0.9873046875}, {"start": 3284.25, "end": 3284.73, "word": ".5.", "probability": 0.995361328125}, {"start": 3285.31, "end": 3285.63, "word": " Now,", "probability": 0.94580078125}, {"start": 3286.79, "end": 3287.13, "word": " any", "probability": 0.89208984375}, {"start": 3287.13, "end": 3287.47, "word": " point", "probability": 0.9716796875}, {"start": 3287.47, "end": 3287.71, "word": " or", "probability": 0.7939453125}, {"start": 3287.71, "end": 3287.95, "word": " any", "probability": 0.9228515625}, {"start": 3287.95, "end": 3288.21, "word": " data", "probability": 0.9423828125}, {"start": 3288.21, "end": 3288.57, "word": " value,", "probability": 0.89892578125}, {"start": 3289.45, "end": 3291.09, "word": " any", "probability": 0.79150390625}, {"start": 3291.09, "end": 3291.39, "word": " data", "probability": 0.9384765625}, {"start": 3291.39, "end": 3291.81, "word": " value", "probability": 0.96630859375}, {"start": 3291.81, "end": 3293.97, "word": " falls", "probability": 0.6630859375}, {"start": 3293.97, "end": 3294.59, "word": " below", "probability": 0.91796875}, {"start": 3294.59, "end": 3295.01, "word": " minus", "probability": 0.96484375}, {"start": 3295.01, "end": 3295.23, "word": " 2", "probability": 0.98291015625}, {"start": 3295.23, "end": 3295.63, "word": ".5.", "probability": 0.9990234375}, {"start": 3295.71, "end": 3295.81, "word": " I", "probability": 0.96630859375}, {"start": 3295.81, "end": 3295.95, "word": " mean", "probability": 0.9619140625}, {"start": 3295.95, "end": 3296.39, "word": " smaller", "probability": 0.39208984375}, {"start": 3296.39, "end": 3296.71, "word": " than", "probability": 0.93603515625}, {"start": 3296.71, "end": 3297.03, "word": " minus", "probability": 0.98193359375}, {"start": 3297.03, "end": 3297.23, "word": " 2", "probability": 0.99853515625}, {"start": 3297.23, "end": 3297.69, "word": ".5.", "probability": 0.999755859375}], "temperature": 1.0}, {"id": 121, "seek": 332526, "start": 3298.3, "end": 3325.26, "text": " Or greater than 9.5 is an outlier. If you look at the data you have, we have 0 up to 9. So none of these is considered to be an outlier. But what's about 27? 27 is greater than, much bigger than actually 9.5. So for that data, 27 is an outlier.", "tokens": [1610, 5044, 813, 1722, 13, 20, 307, 364, 484, 2753, 13, 759, 291, 574, 412, 264, 1412, 291, 362, 11, 321, 362, 1958, 493, 281, 1722, 13, 407, 6022, 295, 613, 307, 4888, 281, 312, 364, 484, 2753, 13, 583, 437, 311, 466, 7634, 30, 7634, 307, 5044, 813, 11, 709, 3801, 813, 767, 1722, 13, 20, 13, 407, 337, 300, 1412, 11, 7634, 307, 364, 484, 2753, 13], "avg_logprob": -0.14352679188762393, "compression_ratio": 1.53125, "no_speech_prob": 0.0, "words": [{"start": 3298.3, "end": 3298.58, "word": " Or", "probability": 0.39697265625}, {"start": 3298.58, "end": 3298.96, "word": " greater", "probability": 0.771484375}, {"start": 3298.96, "end": 3299.28, "word": " than", "probability": 0.93994140625}, {"start": 3299.28, "end": 3299.5, "word": " 9", "probability": 0.9365234375}, {"start": 3299.5, "end": 3299.98, "word": ".5", "probability": 0.98974609375}, {"start": 3299.98, "end": 3300.22, "word": " is", "probability": 0.8662109375}, {"start": 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way how can we compute the outlier for the sample. Another method. The score is another method to determine if that point is an outlier or not. So, so far we have two rules. One by using quartiles and the other, as we mentioned last time, by using the score. 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"end": 3380.19, "text": " Below minus three. And above three is considered to be irrelevant. That's another example. That's another way to figure out if the data is irrelevant. You can apply the two rules either for the sample or the population. If you have the entire data,", "tokens": [36261, 3175, 1045, 13, 400, 3673, 1045, 307, 4888, 281, 312, 28682, 13, 663, 311, 1071, 1365, 13, 663, 311, 1071, 636, 281, 2573, 484, 498, 264, 1412, 307, 28682, 13, 509, 393, 3079, 264, 732, 4474, 2139, 337, 264, 6889, 420, 264, 4415, 13, 759, 291, 362, 264, 2302, 1412, 11], "avg_logprob": -0.276975247095216, "compression_ratio": 1.55625, "no_speech_prob": 0.0, "words": [{"start": 3356.69, "end": 3357.37, "word": " Below", "probability": 0.3935546875}, {"start": 3357.37, "end": 3357.75, "word": " minus", "probability": 0.92333984375}, {"start": 3357.75, "end": 3358.01, "word": " three.", "probability": 0.78125}, {"start": 3359.15, "end": 3359.57, "word": " And", "probability": 0.9140625}, {"start": 3359.57, "end": 3360.03, "word": " above", "probability": 0.9541015625}, {"start": 3360.03, "end": 3360.53, "word": " three", "probability": 0.73046875}, {"start": 3360.53, "end": 3362.21, "word": " is", "probability": 0.4697265625}, {"start": 3362.21, "end": 3362.57, "word": " considered", "probability": 0.578125}, {"start": 3362.57, "end": 3362.71, "word": " to", "probability": 0.87451171875}, {"start": 3362.71, "end": 3362.79, "word": " be", "probability": 0.93701171875}, {"start": 3362.79, "end": 3362.99, "word": " irrelevant.", "probability": 0.236572265625}, {"start": 3363.11, "end": 3363.43, "word": " That's", "probability": 0.8896484375}, {"start": 3363.43, "end": 3363.69, "word": " another", "probability": 0.93212890625}, {"start": 3363.69, "end": 3364.11, "word": " example.", "probability": 0.8974609375}, {"start": 3364.65, "end": 3364.93, "word": " That's", "probability": 0.950927734375}, {"start": 3364.93, "end": 3365.21, "word": " another", "probability": 0.91796875}, {"start": 3365.21, "end": 3365.57, "word": " way", "probability": 0.953125}, {"start": 3365.57, "end": 3367.03, "word": " to", "probability": 0.93603515625}, {"start": 3367.03, "end": 3367.57, "word": " figure", "probability": 0.9794921875}, {"start": 3367.57, "end": 3367.95, "word": " out", "probability": 0.8603515625}, {"start": 3367.95, "end": 3368.39, "word": " if", "probability": 0.81591796875}, {"start": 3368.39, "end": 3368.55, "word": " the", "probability": 0.38330078125}, {"start": 3368.55, "end": 3368.67, "word": " data", "probability": 0.853515625}, {"start": 3368.67, "end": 3368.87, "word": " is", "probability": 0.62841796875}, {"start": 3368.87, "end": 3369.19, "word": " irrelevant.", "probability": 0.1815185546875}, {"start": 3373.73, "end": 3374.41, "word": " You", "probability": 0.61572265625}, {"start": 3374.41, "end": 3374.71, "word": " can", "probability": 0.63330078125}, {"start": 3374.71, "end": 3375.13, "word": " apply", "probability": 0.9462890625}, {"start": 3375.13, "end": 3375.37, "word": " the", "probability": 0.9111328125}, {"start": 3375.37, "end": 3375.59, "word": " two", "probability": 0.8779296875}, {"start": 3375.59, "end": 3375.97, "word": " rules", "probability": 0.80029296875}, {"start": 3375.97, "end": 3376.37, "word": " either", "probability": 0.80859375}, {"start": 3376.37, "end": 3376.65, "word": " for", "probability": 0.9365234375}, {"start": 3376.65, "end": 3376.83, "word": " the", "probability": 0.85986328125}, {"start": 3376.83, "end": 3377.11, "word": " sample", "probability": 0.6181640625}, {"start": 3377.11, "end": 3377.61, "word": " or", "probability": 0.5205078125}, {"start": 3377.61, "end": 3378.19, "word": " the", "probability": 0.7763671875}, {"start": 3378.19, "end": 3378.57, "word": " population.", "probability": 0.861328125}, {"start": 3378.77, "end": 3378.91, "word": " If", "probability": 0.9619140625}, {"start": 3378.91, "end": 3379.03, "word": " you", "probability": 0.95947265625}, {"start": 3379.03, "end": 3379.19, "word": " have", "probability": 0.912109375}, {"start": 3379.19, "end": 3379.31, "word": " the", "probability": 0.89111328125}, {"start": 3379.31, "end": 3379.69, "word": " entire", "probability": 0.90673828125}, {"start": 3379.69, "end": 3380.19, "word": " data,", "probability": 0.9345703125}], "temperature": 1.0}, {"id": 124, "seek": 340129, "start": 3380.89, "end": 3401.29, "text": " you can also determine out there for the entire dataset, even if that data is the population. But most of the time, we select a sample, which is a subset or a portion of that population. 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