1 00:00:17,750 --> 00:00:21,350 So let's again go back to chapter number one. Last 2 00:00:21,350 --> 00:00:25,730 time we discussed chapter one, production and data 3 00:00:25,730 --> 00:00:32,390 collection. And I think we described why learning 4 00:00:32,390 --> 00:00:36,510 statistics distinguish between some of these 5 00:00:36,510 --> 00:00:43,810 topics. And also we explained in details types of 6 00:00:43,810 --> 00:00:47,010 statistics and we mentioned that statistics mainly 7 00:00:47,010 --> 00:00:52,430 has two types either descriptive statistics which 8 00:00:52,430 --> 00:00:56,810 means collecting summarizing and obtaining data 9 00:00:56,810 --> 00:00:59,910 and other type of statistics is called inferential 10 00:00:59,910 --> 00:01:04,430 statistics or statistical inference and this type 11 00:01:04,430 --> 00:01:11,070 of statistics we can draw drawing conclusions and 12 00:01:11,070 --> 00:01:14,090 making decision concerning a population based only 13 00:01:14,090 --> 00:01:17,510 on a sample. That means we have a sample and 14 00:01:17,510 --> 00:01:20,970 sample is just a subset of the population or the 15 00:01:20,970 --> 00:01:26,230 portion of the population and we use the data from 16 00:01:26,230 --> 00:01:29,130 that sample to make some conclusion about the 17 00:01:29,130 --> 00:01:32,390 entire population. This type of statistic is 18 00:01:32,390 --> 00:01:34,710 called inferential statistics. Later, Inshallah, 19 00:01:34,750 --> 00:01:37,710 we'll talk in details about inferential statistics 20 00:01:37,710 --> 00:01:45,290 that will start in Chapter 7. Also, we gave some 21 00:01:45,290 --> 00:01:50,630 definitions for variables, data, and we 22 00:01:50,630 --> 00:01:53,510 distinguished between population and sample. And 23 00:01:53,510 --> 00:01:56,630 we know that the population consists of all items 24 00:01:56,630 --> 00:02:00,270 or individuals about which you want to draw a 25 00:02:00,270 --> 00:02:05,770 conclusion. But in some cases, it's very hard to 26 00:02:05,770 --> 00:02:07,750 talk about the population or the entire 27 00:02:07,750 --> 00:02:13,340 population, so we can select a sample. A sample is 28 00:02:13,340 --> 00:02:18,480 just a portion or subset of the entire population. 29 00:02:19,060 --> 00:02:21,860 So we know now the definition of population and 30 00:02:21,860 --> 00:02:25,360 sample. The other two types, parameter and 31 00:02:25,360 --> 00:02:28,860 statistics. Parameter is a numerical measure that 32 00:02:28,860 --> 00:02:32,300 describes characteristics of a population, while 33 00:02:32,300 --> 00:02:36,000 on the other hand, a sample, a statistic is just 34 00:02:36,430 --> 00:02:39,730 numerical measures that describe characteristic of 35 00:02:39,730 --> 00:02:44,930 a sample. So parameter is computed from the 36 00:02:44,930 --> 00:02:48,930 population while statistic is computed from the 37 00:02:48,930 --> 00:02:54,030 sample. I think we stopped at this point. Why 38 00:02:54,030 --> 00:02:56,770 collect data? I mean what are the reasons for 39 00:02:59,580 --> 00:03:01,980 One of these reasons, for example, a marketing 40 00:03:01,980 --> 00:03:04,660 research analyst needs to assess the effectiveness 41 00:03:04,660 --> 00:03:07,700 of a new television advertisement. For example, 42 00:03:07,840 --> 00:03:13,380 suppose you are a manager and you want to increase 43 00:03:13,380 --> 00:03:18,060 your salaries or your sales. Now, sales may be 44 00:03:18,060 --> 00:03:23,380 affected by advertising. So I mean, if you spend 45 00:03:23,380 --> 00:03:26,320 more on advertising, it means your sales becomes 46 00:03:26,320 --> 00:03:29,740 larger and larger. So you want to know if this 47 00:03:29,740 --> 00:03:34,160 variable, I mean if advertisement is an effective 48 00:03:34,160 --> 00:03:38,900 variable that maybe increase your sales. So that's 49 00:03:38,900 --> 00:03:43,900 one of the reasons why we use data. The other one, 50 00:03:44,120 --> 00:03:46,880 for example, pharmaceutical manufacturers needs to 51 00:03:46,880 --> 00:03:49,800 determine whether a new drug is more effective 52 00:03:49,800 --> 00:03:53,240 than those currently used. For example, for a 53 00:03:53,240 --> 00:03:59,330 headache, we use drug A. Now, a new drug is 54 00:03:59,330 --> 00:04:04,510 produced and you want to see if this new drug is 55 00:04:04,510 --> 00:04:10,090 more effective than drug A that I mean if headache 56 00:04:10,090 --> 00:04:13,410 suppose for example is removed after three days by 57 00:04:13,410 --> 00:04:20,490 using drug A now the question is does B is more 58 00:04:20,490 --> 00:04:23,410 effective it means it reduces your headache in 59 00:04:23,410 --> 00:04:26,070 fewer than three days I mean maybe in two days 60 00:04:26,510 --> 00:04:30,810 That means a drug B is more effective than a drug 61 00:04:30,810 --> 00:04:34,510 A. So we want to know the difference between these 62 00:04:34,510 --> 00:04:37,250 two drugs. I mean, we have two samples. Some 63 00:04:37,250 --> 00:04:40,810 people used drug A and the other used drug B. And 64 00:04:40,810 --> 00:04:43,190 we want to see if there is a significant 65 00:04:43,190 --> 00:04:47,690 difference between the times that is used to 66 00:04:47,690 --> 00:04:51,150 reduce the headache. So that's one of the reasons 67 00:04:51,150 --> 00:04:55,260 why we use statistics. Sometimes an operation 68 00:04:55,260 --> 00:04:58,500 manager wants to monitor manufacturing process to 69 00:04:58,500 --> 00:05:00,720 find out whether the quality of a product being 70 00:05:00,720 --> 00:05:02,840 manufactured is conforming to a company's 71 00:05:02,840 --> 00:05:05,700 standards. Do you know what the meaning of 72 00:05:05,700 --> 00:05:06,520 company's standards? 73 00:05:09,900 --> 00:05:15,320 The regulations of the firm itself. Another 74 00:05:15,320 --> 00:05:21,020 example, suppose here in the school last year, we 75 00:05:21,020 --> 00:05:25,150 teach statistics by using method A. traditional 76 00:05:25,150 --> 00:05:29,350 method. This year we developed a new method for 77 00:05:29,350 --> 00:05:32,370 teaching and our goal is to see if the new method 78 00:05:32,370 --> 00:05:36,510 is better than method A which was used in last 79 00:05:36,510 --> 00:05:38,910 year. So we want to see if there is a big 80 00:05:38,910 --> 00:05:42,410 difference between scores or the average scores 81 00:05:42,410 --> 00:05:47,310 last year and this year. The same you can do for 82 00:05:47,310 --> 00:05:52,350 your weight. Suppose there are 20 students in this 83 00:05:52,350 --> 00:05:56,960 class and their weights are high. And our goal is 84 00:05:56,960 --> 00:06:04,280 to reduce their weights. Suppose they 85 00:06:04,280 --> 00:06:09,640 have a regime or diet for three months or 86 00:06:09,640 --> 00:06:12,140 exercise, whatever it is, then after three months, 87 00:06:12,220 --> 00:06:17,060 we have new weights for these persons. And we want 88 00:06:17,060 --> 00:06:19,840 to see if the diet is effective. I mean, if the 89 00:06:19,840 --> 00:06:24,120 average weight was greater than or smaller than 90 00:06:24,120 --> 00:06:28,600 before diet. Is it clear? So there are many, many 91 00:06:28,600 --> 00:06:31,920 reasons behind using statistics and collecting 92 00:06:31,920 --> 00:06:37,500 data. Now, what are the sources of data? Since 93 00:06:37,500 --> 00:06:41,840 statistics mainly, first step, we have to collect 94 00:06:41,840 --> 00:06:44,120 data. Now, what are the sources of the data? 95 00:06:45,360 --> 00:06:48,420 Generally speaking, there are two sources. One is 96 00:06:48,420 --> 00:06:52,430 called The primary sources and the others 97 00:06:52,430 --> 00:06:55,770 secondary sources. What do you think is the 98 00:06:55,770 --> 00:06:57,830 difference between these two? I mean, what's the 99 00:06:57,830 --> 00:07:02,730 difference between primary and secondary sources? 100 00:07:03,510 --> 00:07:07,250 The primary source is the collector of the data. 101 00:07:07,670 --> 00:07:11,550 He is the analyzer. He analyzes it. And then the 102 00:07:11,550 --> 00:07:14,230 secondary, who collects the data, isn't there. 103 00:07:16,030 --> 00:07:18,910 That's correct. So the primary sources means the 104 00:07:18,910 --> 00:07:22,490 researcher by himself. He should collect the data, 105 00:07:23,890 --> 00:07:27,750 then he can use the data to do his analysis. 106 00:07:28,310 --> 00:07:31,550 That's for the primary. Now, the primary could be 107 00:07:31,550 --> 00:07:35,230 data from political survey. You can distribute 108 00:07:35,230 --> 00:07:38,750 questionnaire, for example, data collected from an 109 00:07:38,750 --> 00:07:42,530 experiment. I mean maybe control or experimental 110 00:07:42,530 --> 00:07:45,730 groups. We have two groups, maybe healthy people 111 00:07:45,730 --> 00:07:48,490 and patient people. So that's experimental group. 112 00:07:49,010 --> 00:07:53,390 Or observed data. That's the primary sources. 113 00:07:53,870 --> 00:07:56,450 Secondary sources, the person performing data 114 00:07:56,450 --> 00:08:00,310 analysis is not the data collector. So he obtained 115 00:08:00,310 --> 00:08:03,880 the data from other sources. For example, it could 116 00:08:03,880 --> 00:08:07,140 be analyzing census data or for example, examining 117 00:08:07,140 --> 00:08:10,160 data from print journals or data published on the 118 00:08:10,160 --> 00:08:14,780 internet. So maybe he goes to the Ministry of 119 00:08:14,780 --> 00:08:18,820 Education and he can get some data. So the data is 120 00:08:18,820 --> 00:08:22,520 already there and he just used the data to do some 121 00:08:22,520 --> 00:08:25,540 analysis. So that's the difference between a 122 00:08:25,540 --> 00:08:29,420 primary and secondary sources. So primary, the 123 00:08:29,420 --> 00:08:33,650 researcher himself, should collect the data by 124 00:08:33,650 --> 00:08:35,590 using one of the tools, either survey, 125 00:08:36,110 --> 00:08:39,050 questionnaire, experiment, and so on. But 126 00:08:39,050 --> 00:08:41,450 secondary, you can use the data that is published 127 00:08:41,450 --> 00:08:44,510 in the internet, for example, in the books, in 128 00:08:44,510 --> 00:08:48,250 governments and NGOs and so on. So these are the 129 00:08:48,250 --> 00:08:53,590 two sources of data. Sources of data fall into 130 00:08:53,590 --> 00:08:57,610 four categories. Number one, data distributed by 131 00:08:57,610 --> 00:09:01,190 an organization or an individual. So that's 132 00:09:01,190 --> 00:09:06,170 secondary source. A design experiment is primary 133 00:09:06,170 --> 00:09:10,350 because you have to design the experiment, a 134 00:09:10,350 --> 00:09:14,610 survey. It's also primary. An observational study 135 00:09:14,610 --> 00:09:17,590 is also a primary source. So you have to 136 00:09:17,590 --> 00:09:21,410 distinguish between a primary and secondary 137 00:09:21,410 --> 00:09:28,810 sources. Any question? Comments? Next. 138 00:09:31,460 --> 00:09:34,540 We'll talk a little bit about types of variables. 139 00:09:35,360 --> 00:09:37,580 In general, there are two types of variables. One 140 00:09:37,580 --> 00:09:40,760 is called categorical variables or qualitative 141 00:09:40,760 --> 00:09:43,160 variables, and the other one is called numerical 142 00:09:43,160 --> 00:09:46,520 or quantitative variables. Now, for example, if I 143 00:09:46,520 --> 00:09:50,560 ask you, what's 144 00:09:50,560 --> 00:09:55,100 your favorite color? You may say white, black, 145 00:09:55,220 --> 00:09:59,390 red, and so on. What's your marital status? Maybe 146 00:09:59,390 --> 00:10:02,670 married or unmarried, and so on. Gender, male, 147 00:10:02,850 --> 00:10:07,050 either male or female, and so on. So this type of 148 00:10:07,050 --> 00:10:10,090 variable is called qualitative variables. So 149 00:10:10,090 --> 00:10:13,130 qualitative variables have values that can only be 150 00:10:13,130 --> 00:10:16,370 placed into categories, such as, for example, yes 151 00:10:16,370 --> 00:10:21,350 or no. For example, do you like orange? 152 00:10:22,270 --> 00:10:26,200 The answer is either yes or no. Do you like 153 00:10:26,200 --> 00:10:30,040 candidate A, for example, whatever his party is? 154 00:10:30,260 --> 00:10:34,620 Do you like it? Either yes or no, and so on. As I 155 00:10:34,620 --> 00:10:37,480 mentioned before, gender, marital status, race, 156 00:10:37,640 --> 00:10:41,820 religions, these are examples of qualitative or 157 00:10:41,820 --> 00:10:46,240 categorical variables. The other type of variable 158 00:10:46,240 --> 00:10:49,480 which is commonly used is called numerical or 159 00:10:49,480 --> 00:10:53,230 quantitative data. Quantitative variables have 160 00:10:53,230 --> 00:10:56,350 values that represent quantities. For example, if 161 00:10:56,350 --> 00:11:00,470 I ask you, what's your age? My age is 20 years old 162 00:11:00,470 --> 00:11:04,770 or 18 years old. What's your weight? Income. 163 00:11:07,510 --> 00:11:12,550 Height? Temperature? Income. So it's a number. 164 00:11:13,610 --> 00:11:18,030 Weight, maybe my weight is 70 kilograms. So 165 00:11:18,030 --> 00:11:22,450 weight, age, height, salary, income, number of 166 00:11:22,450 --> 00:11:26,510 students, number of phone calls you received on 167 00:11:26,510 --> 00:11:28,770 your cell phone during one hour, number of 168 00:11:28,770 --> 00:11:33,210 accidents happened in street and so on. So that's 169 00:11:33,210 --> 00:11:36,470 the difference between numerical variables and 170 00:11:36,470 --> 00:11:37,710 qualitative variables. 171 00:11:40,270 --> 00:11:42,650 Anyone of you just give me one example of 172 00:11:42,650 --> 00:11:47,780 qualitative and quantitative variables. Another 173 00:11:47,780 --> 00:11:51,700 examples. Just give me one example for qualitative 174 00:11:51,700 --> 00:11:52,160 data. 175 00:11:56,900 --> 00:11:58,780 Qualitative or quantitative. 176 00:12:01,380 --> 00:12:04,880 Political party, either party A or party B. So 177 00:12:04,880 --> 00:12:08,320 suppose there are two parties, so I like party A, 178 00:12:08,720 --> 00:12:12,320 she likes party B and so on. So party in this case 179 00:12:12,320 --> 00:12:15,060 is qualitative variable, another one. 180 00:12:25,400 --> 00:12:28,820 So types of courses, maybe business, economics, 181 00:12:29,480 --> 00:12:33,260 administration, and so on. So types of courses. 182 00:12:34,260 --> 00:12:36,600 Another example for quantitative variable or 183 00:12:36,600 --> 00:12:37,600 numerical variables. 184 00:12:45,020 --> 00:12:51,440 So production is a numerical variable. Another 185 00:12:51,440 --> 00:12:52,840 example for quantitative. 186 00:12:56,350 --> 00:12:58,970 Is that produced by this company? Number of cell 187 00:12:58,970 --> 00:13:03,950 phones, maybe 20, 17, and so on. Any question? 188 00:13:06,190 --> 00:13:12,410 Next. So generally speaking, types of data, data 189 00:13:12,410 --> 00:13:17,960 has two types, categorical and numerical data. As 190 00:13:17,960 --> 00:13:21,240 we mentioned, marital status, political party, eye 191 00:13:21,240 --> 00:13:25,120 color, and so on. These are examples of 192 00:13:25,120 --> 00:13:28,180 categorical variables. On the other hand, a 193 00:13:28,180 --> 00:13:30,720 numerical variable can be split or divided into 194 00:13:30,720 --> 00:13:34,020 two parts. One is called discrete and the other is 195 00:13:34,020 --> 00:13:35,680 continuous, and we have to distinguish between 196 00:13:35,680 --> 00:13:40,240 these two. For example, Number of students in this 197 00:13:40,240 --> 00:13:43,400 class, you can say there are 60 or 50 students in 198 00:13:43,400 --> 00:13:47,260 this class. You cannot say there are 50.5 199 00:13:47,260 --> 00:13:52,160 students. So number of students is discrete 200 00:13:52,160 --> 00:13:57,040 because it takes only integers. While for 201 00:13:57,040 --> 00:13:59,800 continuous type of numerical variables, you can 202 00:13:59,800 --> 00:14:06,060 say that my weight is 80.5 kilograms. so it makes 203 00:14:06,060 --> 00:14:09,260 sense that your weight is not exactly 80 kilograms 204 00:14:09,260 --> 00:14:15,580 it might be 80.6 or 80.5 and so on so discrete 205 00:14:15,580 --> 00:14:20,420 takes only integers while continuous takes any 206 00:14:20,420 --> 00:14:24,140 value I mean any real number so that's the 207 00:14:24,140 --> 00:14:28,980 difference between discrete and continuous number 208 00:14:28,980 --> 00:14:33,930 of phone or number of calls you have received this 209 00:14:33,930 --> 00:14:37,670 morning, maybe one, zero, nine, and so on, 210 00:14:38,390 --> 00:14:41,950 discrete. Number of patients in the hospital, 211 00:14:42,350 --> 00:14:46,590 discrete, and so on. But when we are talking about 212 00:14:46,590 --> 00:14:50,850 income, maybe my income is 1,000.5 shekel. It 213 00:14:50,850 --> 00:14:55,790 could be. It's continuous because my income can be 214 00:14:55,790 --> 00:14:59,210 any number between, for example, 1,000 and 10,000. 215 00:15:00,470 --> 00:15:03,550 It takes any value in this interval from 1,000 to 216 00:15:03,550 --> 00:15:08,410 10,000. So it types of continuous rather than our 217 00:15:08,410 --> 00:15:12,450 continuous variable. So that's the two types of 218 00:15:12,450 --> 00:15:15,590 data, categorical and numerical. And numerical 219 00:15:15,590 --> 00:15:18,510 also has two types, either discrete or continuous. 220 00:15:19,750 --> 00:15:24,430 Later in Chapter 6, we'll talk more details about 221 00:15:24,430 --> 00:15:28,940 one of the most distribution statistics, for 222 00:15:28,940 --> 00:15:31,560 continuous, one which is called normal 223 00:15:31,560 --> 00:15:36,240 distribution. That will be later, inshallah. As we 224 00:15:36,240 --> 00:15:39,000 mentioned last time, at the end of each chapter, 225 00:15:39,280 --> 00:15:41,640 there is a section or sections, sometimes there 226 00:15:41,640 --> 00:15:45,000 are two sections, talks about computer programs. 227 00:15:45,120 --> 00:15:49,200 How can we use computer programs in order to 228 00:15:49,200 --> 00:15:52,300 analyze the data? And as we mentioned last time, 229 00:15:52,420 --> 00:15:54,600 you should take a course on that. It's called 230 00:15:54,600 --> 00:15:57,960 Computer and Data Analysis or SPSS course. So we 231 00:15:57,960 --> 00:16:03,860 are going to skip the computer programs used for 232 00:16:03,860 --> 00:16:08,720 any chapters in this book. And that's the end of 233 00:16:08,720 --> 00:16:13,060 chapter number three. Any questions? 234 00:16:18,380 --> 00:16:22,550 Let's move. quickly on chapter three. 235 00:16:31,290 --> 00:16:35,530 Chapter three maybe is the easiest chapter in this 236 00:16:35,530 --> 00:16:39,950 book. It's straightforward. We have some formulas 237 00:16:39,950 --> 00:16:45,280 to compute some statistical measures. And we 238 00:16:45,280 --> 00:16:47,400 should know how can we calculate these measures 239 00:16:47,400 --> 00:16:52,620 and what are the meaning of your results. So 240 00:16:52,620 --> 00:16:56,140 chapter three talks about numerical descriptive 241 00:16:56,140 --> 00:17:03,220 measures. In this chapter, you will learn, number 242 00:17:03,220 --> 00:17:06,480 one, describe the probabilities of central 243 00:17:06,480 --> 00:17:11,880 tendency, variation, and shape in numerical data. 244 00:17:12,730 --> 00:17:16,250 In this lecture, we'll talk in more details about 245 00:17:16,250 --> 00:17:21,370 some of the center tendency measures. Later, we'll 246 00:17:21,370 --> 00:17:26,490 talk about the variation, or spread, or 247 00:17:26,490 --> 00:17:29,690 dispersion, and the shape in numerical data. So 248 00:17:29,690 --> 00:17:31,630 that's part number one. We have to know something 249 00:17:31,630 --> 00:17:36,390 about center tendency, variation, and the shape of 250 00:17:36,390 --> 00:17:42,020 the data we have. to calculate descriptive summary 251 00:17:42,020 --> 00:17:45,360 measures for a population. So we have to calculate 252 00:17:45,360 --> 00:17:48,460 these measures for the sample. And if we have the 253 00:17:48,460 --> 00:17:51,420 entire population, we can compute these measures 254 00:17:51,420 --> 00:17:58,440 also for that population. Then I will introduce in 255 00:17:58,440 --> 00:18:01,920 more details about something called Paxiplot. How 256 00:18:01,920 --> 00:18:06,660 can we construct and interpret a Paxiplot? That's, 257 00:18:06,960 --> 00:18:11,040 inshallah, next time on Tuesday. Finally, we'll 258 00:18:11,040 --> 00:18:13,020 see how can we calculate the covariance and 259 00:18:13,020 --> 00:18:15,700 coefficient of variation and coefficient, I'm 260 00:18:15,700 --> 00:18:18,480 sorry, coefficient of correlation. This topic 261 00:18:18,480 --> 00:18:24,280 we'll introduce in more details in chapter 11 262 00:18:24,280 --> 00:18:31,240 later on. So just I will give some brief 263 00:18:31,240 --> 00:18:35,630 notation about coefficient of correlation, how can 264 00:18:35,630 --> 00:18:39,030 we compute the correlation coefficient? What's the 265 00:18:39,030 --> 00:18:41,870 meaning of your result? And later in chapter 11, 266 00:18:42,030 --> 00:18:44,510 we'll talk in more details about correlation and 267 00:18:44,510 --> 00:18:48,930 regression. So these are the objectives of this 268 00:18:48,930 --> 00:18:52,870 chapter. There are some basic definitions before 269 00:18:52,870 --> 00:18:57,410 we start. One is called central tendency. What do 270 00:18:57,410 --> 00:19:00,750 you mean by central tendency? Central tendency is 271 00:19:00,750 --> 00:19:04,990 the extent to which all data value group around a 272 00:19:04,990 --> 00:19:08,890 typical or numerical or central value. So we are 273 00:19:08,890 --> 00:19:12,510 looking for a point that in the center, I mean, 274 00:19:12,810 --> 00:19:18,870 the data points are gathered or collected around a 275 00:19:18,870 --> 00:19:21,670 middle point, and that middle point is called the 276 00:19:21,670 --> 00:19:24,450 central tendency. And the question is, how can we 277 00:19:24,450 --> 00:19:27,780 measure that value? We'll talk in details about 278 00:19:27,780 --> 00:19:32,620 mean, median, and mode in a few minutes. So the 279 00:19:32,620 --> 00:19:35,660 central tendency, in this case, the data values 280 00:19:35,660 --> 00:19:40,080 grouped around a typical or central value. Is it 281 00:19:40,080 --> 00:19:44,380 clear? So we have data set, large data set. Then 282 00:19:44,380 --> 00:19:47,860 these points are gathered or grouped around a 283 00:19:47,860 --> 00:19:51,440 middle point, and this point is called central 284 00:19:51,440 --> 00:19:56,120 tendency, and it can be measured by using mean, 285 00:19:56,420 --> 00:19:59,960 which is the most common one, median and the moon. 286 00:20:01,020 --> 00:20:04,480 Next is the variation, which is the amount of 287 00:20:04,480 --> 00:20:09,420 dispersion. Variation is the amount of dispersion 288 00:20:09,420 --> 00:20:13,900 or scattering of values. And we'll use, for 289 00:20:13,900 --> 00:20:18,400 example, range, variance or standard deviation in 290 00:20:18,400 --> 00:20:22,960 order to compute the variation. Finally, We have 291 00:20:22,960 --> 00:20:26,300 data, and my question is, what's the shape of the 292 00:20:26,300 --> 00:20:29,920 data? So the shape is the pattern of distribution 293 00:20:29,920 --> 00:20:35,220 of values from the lowest value to the highest. So 294 00:20:35,220 --> 00:20:39,400 that's the three definitions we need to know 295 00:20:39,400 --> 00:20:44,580 before we start. So we'll start with the easiest 296 00:20:44,580 --> 00:20:48,680 one, measures of central tendency. As I mentioned, 297 00:20:49,160 --> 00:20:55,110 there are three measures. median and moon. And our 298 00:20:55,110 --> 00:20:58,270 goal or we have two goals actually. We have to 299 00:20:58,270 --> 00:21:02,290 know how to compute these measures. Number two, 300 00:21:03,270 --> 00:21:06,390 which one is better? The mean or the median or the 301 00:21:06,390 --> 00:21:06,550 moon? 302 00:21:11,310 --> 00:21:14,770 So the mean sometimes called the arithmetic mean. 303 00:21:15,680 --> 00:21:20,020 Or in general, just say the mean. So often we use 304 00:21:20,020 --> 00:21:26,860 the mean. And the mean is just sum 305 00:21:26,860 --> 00:21:33,220 of the values divided by the sample size. So it's 306 00:21:33,220 --> 00:21:36,800 straightforward. We have, for example, three data 307 00:21:36,800 --> 00:21:42,180 points. And your goal is to find the average or 308 00:21:42,180 --> 00:21:45,890 the mean of these points. They mean it's just some 309 00:21:45,890 --> 00:21:50,230 of these values divided by the sample size. So for 310 00:21:50,230 --> 00:21:54,570 example, if we have a data X1, X2, X3 up to Xn. So 311 00:21:54,570 --> 00:21:59,650 the average is denoted by X bar. This one is 312 00:21:59,650 --> 00:22:04,530 pronounced as X bar and X bar is just sum of Xi. 313 00:22:05,010 --> 00:22:08,250 It is summation, you know this symbol, summation 314 00:22:08,250 --> 00:22:11,350 of sigma, summation of Xi and I goes from one to 315 00:22:11,350 --> 00:22:14,490 N. divided by N which is the total number of 316 00:22:14,490 --> 00:22:19,710 observations or the sample size. So it means X1 317 00:22:19,710 --> 00:22:23,290 plus X2 all the way up to XN divided by N gives 318 00:22:23,290 --> 00:22:28,530 the mean or the arithmetic mean. So X bar is the 319 00:22:28,530 --> 00:22:32,690 average which is the sum of values divided by the 320 00:22:32,690 --> 00:22:36,270 number of observations. So that's the first 321 00:22:36,270 --> 00:22:38,830 definition. For example, 322 00:22:42,180 --> 00:22:46,920 So again, the mean is the most common measure of 323 00:22:46,920 --> 00:22:51,780 center tendency. Number two, the definition of the 324 00:22:51,780 --> 00:22:55,440 mean. Sum of values divided by the number of 325 00:22:55,440 --> 00:23:02,960 values. That means the mean takes all the values, 326 00:23:04,140 --> 00:23:09,740 then divided by N. it makes sense that the mean is 327 00:23:09,740 --> 00:23:13,380 affected by extreme values or outliers. I mean, if 328 00:23:13,380 --> 00:23:17,840 the data has outliers or extreme values, I mean by 329 00:23:17,840 --> 00:23:21,400 extreme values, large or very, very large values 330 00:23:21,400 --> 00:23:24,980 and small, small values. Large values or small 331 00:23:24,980 --> 00:23:31,100 values are extreme values. Since the mean takes 332 00:23:31,100 --> 00:23:33,420 all these values and sums all together, doesn't 333 00:23:33,420 --> 00:23:38,550 divide by n, that means The mean is affected by 334 00:23:38,550 --> 00:23:41,350 outliers or by extreme values. For example, 335 00:23:42,030 --> 00:23:45,110 imagine we have simple data as 1, 2, 3, 4, and 5. 336 00:23:46,110 --> 00:23:49,830 Simple example. Now, what's the mean? The mean is 337 00:23:49,830 --> 00:23:53,570 just add these values, then divide by the total 338 00:23:53,570 --> 00:23:56,910 number of observations. In this case, the sum of 339 00:23:56,910 --> 00:24:01,710 these is 15. N is five because there are five 340 00:24:01,710 --> 00:24:05,920 observations. So X bar is 15 divided by 5, which 341 00:24:05,920 --> 00:24:10,240 is 3. So straightforward. Now imagine instead of 342 00:24:10,240 --> 00:24:16,480 5, this number 5, we have a 10. Now 10, there is a 343 00:24:16,480 --> 00:24:21,400 gap between 4, which is the second largest, and 344 00:24:21,400 --> 00:24:25,600 the maximum, which is 10. Now if we add these 345 00:24:25,600 --> 00:24:30,540 values, 1, 2, 3, 4, and 10, then divide by 5, the 346 00:24:30,540 --> 00:24:36,680 mean will be 4. If you see here, we just added one 347 00:24:36,680 --> 00:24:41,060 value, or I mean, we replaced five by 10, and the 348 00:24:41,060 --> 00:24:44,700 mean changed dramatically from three to four. 349 00:24:45,520 --> 00:24:48,860 There is big change between three and four, around 350 00:24:48,860 --> 00:24:55,560 25% more. So that means outliers or extreme values 351 00:24:55,560 --> 00:25:01,200 affected the mean. So take this information in 352 00:25:01,200 --> 00:25:03,560 your mind because later we'll talk a little bit 353 00:25:03,560 --> 00:25:07,360 about another one. So the mean is affected by 354 00:25:07,360 --> 00:25:13,100 extreme values. Imagine another example. Suppose 355 00:25:13,100 --> 00:25:20,060 we have data from 1 to 9. 1, 2, 3, 4, 6, 7, 8, 9. 356 00:25:21,040 --> 00:25:26,690 Now the mean of these values, some divide by n. If 357 00:25:26,690 --> 00:25:31,970 you sum 1 through 9, summation is 45. Divide by 9, 358 00:25:32,510 --> 00:25:36,230 which is 5. So the sum of these values divided by 359 00:25:36,230 --> 00:25:41,590 N gives the average, so the average is 5. Now 360 00:25:41,590 --> 00:25:46,670 suppose we add 100 to the end of this data. So the 361 00:25:46,670 --> 00:25:53,670 sum will be 145 divided by 10, that's 14.5. Now 362 00:25:53,670 --> 00:25:58,850 the mean was 5. Then after we added 100, it 363 00:25:58,850 --> 00:26:05,470 becomes 14.5. Imagine the mean was 5, it changed 364 00:26:05,470 --> 00:26:11,650 to 14.5. It means around three times. So that 365 00:26:11,650 --> 00:26:17,510 means outliers affect the mean much more than the 366 00:26:17,510 --> 00:26:19,890 other one. We'll talk a little later about it, 367 00:26:19,990 --> 00:26:23,950 which is the median. So keep in mind outliers 368 00:26:25,290 --> 00:26:34,790 affected the mean in this case. Any question? Is 369 00:26:34,790 --> 00:26:41,590 it clear? Yes. So, one more time. The mean is 370 00:26:41,590 --> 00:26:46,990 affected by extreme values. So that's for the 371 00:26:46,990 --> 00:26:50,910 mean. The other measure of center tendency is 372 00:26:50,910 --> 00:26:57,600 called the median. Now, what's the median? What's 373 00:26:57,600 --> 00:27:00,760 the definition of the median from your previous 374 00:27:00,760 --> 00:27:05,880 studies? What's the median? I mean, what's the 375 00:27:05,880 --> 00:27:09,360 definition of the median? Now the middle value, 376 00:27:09,760 --> 00:27:12,980 that's correct, but after we arrange the data from 377 00:27:12,980 --> 00:27:17,040 smallest to largest or largest to smallest, so we 378 00:27:17,040 --> 00:27:20,160 should arrange the data, then we can figure out 379 00:27:20,160 --> 00:27:24,280 the median. So the median is the middle point, but 380 00:27:24,280 --> 00:27:27,060 after we arrange the data from smallest to largest 381 00:27:27,060 --> 00:27:30,030 or vice versa. So that's the definition of the 382 00:27:30,030 --> 00:27:33,930 median. So in an ordered array, so we have to have 383 00:27:33,930 --> 00:27:39,230 order array, the median is the middle number. The 384 00:27:39,230 --> 00:27:42,810 middle number means 50 percent of the data below 385 00:27:42,810 --> 00:27:50,370 and 50 percent above the median because it's 386 00:27:50,370 --> 00:27:52,190 called the median, the value in the middle after 387 00:27:52,190 --> 00:27:55,990 you arrange the data from smallest to largest. 388 00:28:00,130 --> 00:28:02,770 Suppose I again go back to the previous example 389 00:28:02,770 --> 00:28:09,690 when we have data 1, 2, 3, 4, and 5. Now for this 390 00:28:09,690 --> 00:28:14,210 specific example as we did before, now the data is 391 00:28:14,210 --> 00:28:18,670 already ordered. The value in the middle is 3 392 00:28:18,670 --> 00:28:22,330 because there are two pillows. 393 00:28:24,860 --> 00:28:27,300 And also there are the same number of observations 394 00:28:27,300 --> 00:28:33,140 above it. So 3 is the median. Now again imagine we 395 00:28:33,140 --> 00:28:37,320 replace 5, which is the maximum value, by another 396 00:28:37,320 --> 00:28:42,140 one which is extreme one, for example 10. In this 397 00:28:42,140 --> 00:28:47,600 case, the median is still 3. Because the median is 398 00:28:47,600 --> 00:28:49,380 just the value of the middle after you arrange the 399 00:28:49,380 --> 00:28:53,900 data. So it doesn't matter what is the highest or 400 00:28:53,900 --> 00:28:58,860 the maximum value is, the median in this case is 401 00:28:58,860 --> 00:29:03,700 three. It doesn't change. That means the median is 402 00:29:03,700 --> 00:29:08,020 not affected by extreme values. Or to be more 403 00:29:08,020 --> 00:29:12,910 precise, we can say that The median is affected by 404 00:29:12,910 --> 00:29:18,990 outlier, but not the same as the mean. So affect 405 00:29:18,990 --> 00:29:23,610 the mean much more than the median. I mean, you 406 00:29:23,610 --> 00:29:26,550 cannot say for this example, yes, the median is 407 00:29:26,550 --> 00:29:29,310 not affected because the median was three, it 408 00:29:29,310 --> 00:29:33,590 becomes three. But in another examples, there is 409 00:29:33,590 --> 00:29:36,750 small difference between all. 410 00:29:40,770 --> 00:29:44,850 Extreme values affected the mean much more than 411 00:29:44,850 --> 00:29:51,450 the median. If the dataset has extreme values, we 412 00:29:51,450 --> 00:29:54,510 have to use, what do you think, the mean or the 413 00:29:54,510 --> 00:29:58,090 median? The median. So in case or in the presence 414 00:29:58,090 --> 00:30:01,910 of extreme values or outliers, we have to use the 415 00:30:01,910 --> 00:30:07,010 median, not the mean. But in general, we use If 416 00:30:07,010 --> 00:30:10,770 the data is free of outliers, I mean if the data 417 00:30:10,770 --> 00:30:16,410 has not extreme values, then you can use the mean. 418 00:30:16,510 --> 00:30:19,230 The mean is much better than the median in this 419 00:30:19,230 --> 00:30:22,490 case. But if the data has extreme values or 420 00:30:22,490 --> 00:30:27,190 outliers, we should use the median instead of the 421 00:30:27,190 --> 00:30:31,310 mean. Any question? So these are the most common 422 00:30:31,310 --> 00:30:36,710 center tendency measures in statistics, the mean 423 00:30:36,710 --> 00:30:42,390 and the median. And keep in mind, your data should 424 00:30:42,390 --> 00:30:46,170 be numeric. I mean, you cannot use the mean or the 425 00:30:46,170 --> 00:30:50,730 median for qualitative or categorical data, for 426 00:30:50,730 --> 00:30:54,310 example, gender, males or females. You cannot say 427 00:30:54,310 --> 00:30:59,490 the mean of gender or sex is 1.5. It doesn't make 428 00:30:59,490 --> 00:31:05,490 sense. It should be numerical data to use the mean 429 00:31:05,490 --> 00:31:07,590 or the median. So the mean and the median is used 430 00:31:07,590 --> 00:31:11,210 only for numerical data. And we have to 431 00:31:11,210 --> 00:31:14,170 distinguish between mean and median. Mean is used 432 00:31:14,170 --> 00:31:16,870 for data that has not outliers or extreme values, 433 00:31:17,370 --> 00:31:21,450 while the median is used for data that has 434 00:31:21,450 --> 00:31:25,230 outliers or extreme values. Sometimes better to 435 00:31:25,230 --> 00:31:27,990 report both. I mean, sometimes better to report 436 00:31:27,990 --> 00:31:33,450 mean and the median. So you just say the sales for 437 00:31:33,450 --> 00:31:40,560 this company is, for example, $500,000. And the 438 00:31:40,560 --> 00:31:43,900 median, for example, is 550,000. You can see that. 439 00:31:45,680 --> 00:31:46,400 Is it clear? 440 00:31:51,440 --> 00:31:55,560 If you have a small data, it's straightforward and 441 00:31:55,560 --> 00:31:59,180 it's very easy to locate the median. But in case 442 00:31:59,180 --> 00:32:02,120 of large dataset, how can we locate the median? 443 00:32:02,340 --> 00:32:06,640 It's not easy. Just look at the data and you can 444 00:32:06,640 --> 00:32:11,200 say this is the median. It's not easy task. So we 445 00:32:11,200 --> 00:32:15,820 need a rule that locate the median. The location 446 00:32:15,820 --> 00:32:18,020 of the median when the values are in numerical 447 00:32:18,020 --> 00:32:23,580 order from smallest to largest is N plus one 448 00:32:23,580 --> 00:32:26,140 divided by two. That's the position of the median. 449 00:32:26,640 --> 00:32:28,860 If we go back a little bit to the previous 450 00:32:28,860 --> 00:32:34,980 example, here N was five. So the location was 451 00:32:34,980 --> 00:32:40,000 number three, because n plus one divided by two, 452 00:32:40,120 --> 00:32:43,120 five plus one divided by two is three. So location 453 00:32:43,120 --> 00:32:47,340 number three is the median. Location number one is 454 00:32:47,340 --> 00:32:50,840 one, in this case, then two, then three. So 455 00:32:50,840 --> 00:32:53,740 location number three is three. But maybe this 456 00:32:53,740 --> 00:32:57,280 number is not three, and other value maybe 3.1 or 457 00:32:57,280 --> 00:33:02,440 3.2. But the location is number three. Is it 458 00:33:02,440 --> 00:33:08,470 clear? So that's the location. If it is odd, you 459 00:33:08,470 --> 00:33:13,270 mean by odd number, five, seven and so on. So if 460 00:33:13,270 --> 00:33:17,090 the number of values is odd, the median is the 461 00:33:17,090 --> 00:33:21,210 middle number. Now let's imagine if we have even 462 00:33:21,210 --> 00:33:24,570 number of observations. For example, we have one, 463 00:33:24,610 --> 00:33:28,270 two, three, four, five and six. So imagine numbers 464 00:33:28,270 --> 00:33:32,390 from one up to six. What's the median? Now three 465 00:33:32,390 --> 00:33:35,610 is not the median because there are two 466 00:33:35,610 --> 00:33:43,390 observations below three. And three above it. And 467 00:33:43,390 --> 00:33:46,210 four is not the median because three observations 468 00:33:46,210 --> 00:33:53,290 below, two above. So three and four is the middle 469 00:33:53,290 --> 00:33:56,870 value. So just take the average of two middle 470 00:33:56,870 --> 00:34:01,570 points, And that will be the median. So if n is 471 00:34:01,570 --> 00:34:07,990 even, you have to locate two middle points. For 472 00:34:07,990 --> 00:34:10,310 example, n over 2, in this case, we have six 473 00:34:10,310 --> 00:34:13,910 observations. So divide by 2, not n plus 1 divided 474 00:34:13,910 --> 00:34:17,970 by 2, just n over 2. So n over 2 is 3. So place 475 00:34:17,970 --> 00:34:22,930 number 3, and the next one, place number 4, these 476 00:34:22,930 --> 00:34:25,930 are the two middle points. Take the average of 477 00:34:25,930 --> 00:34:32,300 these values, then that's your median. So if N is 478 00:34:32,300 --> 00:34:37,080 even, you have to be careful. You have to find two 479 00:34:37,080 --> 00:34:40,860 middle points and just take the average of these 480 00:34:40,860 --> 00:34:45,100 two. So if N is even, the median is the average of 481 00:34:45,100 --> 00:34:49,200 the two middle numbers. Keep in mind, when we are 482 00:34:49,200 --> 00:34:54,600 saying N plus 2, N plus 2 is just the position of 483 00:34:54,600 --> 00:34:58,670 the median, not the value, location. Not the 484 00:34:58,670 --> 00:35:07,770 value. Is it clear? Any question? So location is 485 00:35:07,770 --> 00:35:10,150 not the value. Location is just the place or the 486 00:35:10,150 --> 00:35:13,450 position of the medium. If N is odd, the position 487 00:35:13,450 --> 00:35:17,710 is N plus one divided by two. If N is even, the 488 00:35:17,710 --> 00:35:20,870 positions of the two middle points are N over two 489 00:35:20,870 --> 00:35:23,090 and the next term or the next point. 490 00:35:28,390 --> 00:35:32,510 Last measure of center tendency is called the 491 00:35:32,510 --> 00:35:32,750 mood. 492 00:35:35,890 --> 00:35:39,010 The definition of the mood, the mood is the most 493 00:35:39,010 --> 00:35:44,250 frequent value. So sometimes the mood exists, 494 00:35:45,230 --> 00:35:48,570 sometimes the mood does not exist. Or sometimes 495 00:35:48,570 --> 00:35:53,730 there is only one mood, in other cases maybe there 496 00:35:53,730 --> 00:35:58,730 are several moods. So a value that occurs most 497 00:35:58,730 --> 00:36:03,010 often is called the mood. The mood is not affected 498 00:36:03,010 --> 00:36:07,610 by extreme values. It can be used for either 499 00:36:07,610 --> 00:36:11,190 numerical or categorical data. And that's the 500 00:36:11,190 --> 00:36:13,910 difference between mean and median and the mood. 501 00:36:14,590 --> 00:36:16,930 Mean and median is used just for numerical data. 502 00:36:17,430 --> 00:36:21,270 Here, the mood can be used for both, categorical 503 00:36:21,270 --> 00:36:25,610 and numerical data. Sometimes, as I mentioned, 504 00:36:25,930 --> 00:36:29,570 there may be no mood or the mood does not exist. 505 00:36:30,130 --> 00:36:34,190 In other cases, there may be several events. So 506 00:36:34,190 --> 00:36:36,870 the mood is the value that has the most frequent. 507 00:36:37,490 --> 00:36:43,650 For example, if you look at this data, one is 508 00:36:43,650 --> 00:36:48,370 repeated once, three is the same one time, five is 509 00:36:48,370 --> 00:36:52,290 repeated twice. seven is one nine is repeated 510 00:36:52,290 --> 00:36:57,330 three times and so on so in this case nine is the 511 00:36:57,330 --> 00:37:00,290 mood because the mood again is the most frequent 512 00:37:00,290 --> 00:37:05,030 value on 513 00:37:05,030 --> 00:37:08,550 the right side there are some values zero one two 514 00:37:08,550 --> 00:37:12,830 three up to six now each one is repeated once so 515 00:37:12,830 --> 00:37:15,350 in this case the mood does not exist I mean there 516 00:37:15,350 --> 00:37:22,310 is no mood So generally speaking, the mood is the 517 00:37:22,310 --> 00:37:26,310 value that you care most often. It can be used for 518 00:37:26,310 --> 00:37:29,790 numerical or categorical data, not affected by 519 00:37:29,790 --> 00:37:32,970 extreme values or outliers. Sometimes there is 520 00:37:32,970 --> 00:37:36,150 only one mood as this example. Sometimes the mood 521 00:37:36,150 --> 00:37:40,390 does not exist. Or sometimes there are several 522 00:37:40,390 --> 00:37:45,190 moods. And so that's the definitions for mean, 523 00:37:46,430 --> 00:37:52,540 median, and the mood. I will give just a numerical 524 00:37:52,540 --> 00:37:56,380 example to know how can we compute these measures. 525 00:37:57,420 --> 00:38:01,540 This data, simple data, just for illustration, we 526 00:38:01,540 --> 00:38:07,580 have house prices. We have five data points, $2 527 00:38:07,580 --> 00:38:10,940 million. This is the price of house A, for 528 00:38:10,940 --> 00:38:15,880 example. House B price is 500,000. The other one 529 00:38:15,880 --> 00:38:19,120 is 300,000. And two houses have the same price as 530 00:38:19,120 --> 00:38:25,850 100,000. Now, just to compute the mean, add these 531 00:38:25,850 --> 00:38:29,350 values or sum these values, which is three 532 00:38:29,350 --> 00:38:34,030 million, divide by number of houses here, there 533 00:38:34,030 --> 00:38:38,550 are five houses, so just three thousand divided by 534 00:38:38,550 --> 00:38:44,170 five, six hundred thousand. The median, the value 535 00:38:44,170 --> 00:38:46,150 in the median, after you arrange the data from 536 00:38:46,150 --> 00:38:51,470 smallest to largest, Or largest smallest. This 537 00:38:51,470 --> 00:38:55,410 data is already arranged from largest smallest or 538 00:38:55,410 --> 00:38:58,150 smallest large. It doesn't matter actually. So the 539 00:38:58,150 --> 00:39:02,930 median is $300,000. Make sense? Because there are 540 00:39:02,930 --> 00:39:09,490 two house prices above and two below. So the 541 00:39:09,490 --> 00:39:13,610 median is $300,000. Now if you look at these two 542 00:39:13,610 --> 00:39:21,350 values, the mean for this data equals 600,000 and 543 00:39:21,350 --> 00:39:26,690 the median is 300,000. The mean is double the 544 00:39:26,690 --> 00:39:31,750 median. Do you think why there is a big difference 545 00:39:31,750 --> 00:39:36,030 in this data between the mean and the median? 546 00:39:36,190 --> 00:39:42,290 Which one? Two million dollars is extreme value, 547 00:39:42,510 --> 00:39:45,940 very large number. I mean, if you compare two 548 00:39:45,940 --> 00:39:48,860 million dollars with the other data sets or other 549 00:39:48,860 --> 00:39:51,320 data values, you will see there is a big 550 00:39:51,320 --> 00:39:53,260 difference between two million and five hundred. 551 00:39:53,620 --> 00:39:56,280 It's four times, plus about three hundred 552 00:39:56,280 --> 00:39:59,780 thousands, around seven times and so on. For this 553 00:39:59,780 --> 00:40:07,880 value, the mean is affected. Exactly. The median 554 00:40:07,880 --> 00:40:11,740 is resistant to outliers. It's affected but little 555 00:40:11,740 --> 00:40:17,100 bit. For this reason, we have to use the median. 556 00:40:17,300 --> 00:40:20,720 So the median makes more sense than using the 557 00:40:20,720 --> 00:40:24,480 mean. The mode is just the most frequent value, 558 00:40:24,660 --> 00:40:28,720 which is 100,000, because this value is repeated 559 00:40:28,720 --> 00:40:33,820 twice. So that's the whole story for central 560 00:40:33,820 --> 00:40:40,720 tendency measures, mean, median, and 1. Now the 561 00:40:40,720 --> 00:40:45,640 question again is which measure to use? The mean 562 00:40:45,640 --> 00:40:49,280 is generally used. The most common center tendency 563 00:40:49,280 --> 00:40:53,420 is the mean. We can use it or we should use it 564 00:40:53,420 --> 00:40:59,920 unless extreme values exist. I mean if the data 565 00:40:59,920 --> 00:41:03,960 set has no outliers or extreme values, we have to 566 00:41:03,960 --> 00:41:06,240 use the mean instead of the median. 567 00:41:09,810 --> 00:41:14,670 The median is often used since the median is not 568 00:41:14,670 --> 00:41:18,330 sensitive to extreme values. I mean, the median is 569 00:41:18,330 --> 00:41:22,030 resistant to outliers. It remains nearly in the 570 00:41:22,030 --> 00:41:26,490 same position if the dataset has outliers. But the 571 00:41:26,490 --> 00:41:29,850 median will be affected either to the right or to 572 00:41:29,850 --> 00:41:34,350 the left tail. So we have to use the median if the 573 00:41:34,350 --> 00:41:40,060 data has extreme values. For example, median home 574 00:41:40,060 --> 00:41:44,100 prices for the previous one may be reported for a 575 00:41:44,100 --> 00:41:48,000 region that is less sensitive to outliers. So the 576 00:41:48,000 --> 00:41:52,880 mean is more sensitive to outliers than the 577 00:41:52,880 --> 00:41:56,520 median. Sometimes, I mean in some situations, it 578 00:41:56,520 --> 00:41:58,760 makes sense to report both the mean and the 579 00:41:58,760 --> 00:42:01,860 median. Just say the mean for this data for home 580 00:42:01,860 --> 00:42:07,570 prices is 600,000 while the median is 300,000. If 581 00:42:07,570 --> 00:42:10,150 you look at these two figures, you can tell that 582 00:42:10,150 --> 00:42:13,830 there exists outlier or the outlier exists because 583 00:42:13,830 --> 00:42:17,230 there is a big difference between the mean and the 584 00:42:17,230 --> 00:42:24,310 median. So that's all for measures of central 585 00:42:24,310 --> 00:42:28,830 tendency. Again, we explained three measures, 586 00:42:29,450 --> 00:42:33,930 arithmetic mean, median, and mode. And arithmetic 587 00:42:33,930 --> 00:42:38,990 mean again is denoted by X bar is pronounced as X 588 00:42:38,990 --> 00:42:44,410 bar and just summation of X divided by N. So 589 00:42:44,410 --> 00:42:48,070 summation Xi, i goes from 1 up to N divided by the 590 00:42:48,070 --> 00:42:52,170 total number of observations. The median, as we 591 00:42:52,170 --> 00:42:55,690 mentioned, is the value in the middle in ordered 592 00:42:55,690 --> 00:42:59,150 array. After you arrange the data from smallest to 593 00:42:59,150 --> 00:43:01,930 largest or vice versa, then the median is the 594 00:43:01,930 --> 00:43:06,330 value in the middle. The mode is the most frequent 595 00:43:06,330 --> 00:43:09,030 observed value. And we have to know that mean and 596 00:43:09,030 --> 00:43:13,870 median are used only for numerical data, while the 597 00:43:13,870 --> 00:43:17,510 mode can be used for both numerical and 598 00:43:17,510 --> 00:43:24,290 categorical data. That's all about measures of 599 00:43:24,290 --> 00:43:27,210 central tendency. Any question? 600 00:43:33,210 --> 00:43:40,230 Let's move to measures of variation. It's another 601 00:43:40,230 --> 00:43:43,750 type of measures. It's called measures of 602 00:43:43,750 --> 00:43:47,490 variation, sometimes called measures of spread. 603 00:43:50,490 --> 00:43:53,850 Now, variation can be computed by using range, 604 00:43:55,590 --> 00:44:00,850 variance, standard deviation, and coefficient of 605 00:44:00,850 --> 00:44:08,430 variation. So we have four types, range, variance, 606 00:44:09,250 --> 00:44:12,050 standard deviation, and coefficient of variation. 607 00:44:13,710 --> 00:44:16,150 Now, measures of variation give information on the 608 00:44:16,150 --> 00:44:19,410 spread. Now, this is the first difference between 609 00:44:19,410 --> 00:44:24,210 central tendency measures and measures of 610 00:44:24,210 --> 00:44:28,270 variation. That one measures the central value or 611 00:44:28,270 --> 00:44:30,790 the value in the middle. Here, it measures the 612 00:44:30,790 --> 00:44:36,310 spread. Or variability. Or dispersion of the data. 613 00:44:36,450 --> 00:44:40,310 Do you know what is dispersion? Dispersion. 614 00:44:40,630 --> 00:44:45,590 Tabaad. So major variation given formation with 615 00:44:45,590 --> 00:44:48,350 the spread. Spread or variation or dispersion of 616 00:44:48,350 --> 00:44:52,250 the data values. Now if you look at these two bell 617 00:44:52,250 --> 00:44:52,650 shapes. 618 00:44:55,670 --> 00:44:59,170 Both have the same center. The center I mean the 619 00:44:59,170 --> 00:45:01,730 value in the middle. So the value in the middle 620 00:45:01,730 --> 00:45:06,990 here for figure 621 00:45:06,990 --> 00:45:10,150 graph number one is the same as the value for the 622 00:45:10,150 --> 00:45:16,270 other graph. So both graphs have the same center. 623 00:45:17,430 --> 00:45:20,670 But if you look at the spread, you will see that 624 00:45:20,670 --> 00:45:26,230 figure A is less spread than figure B. Now if you 625 00:45:26,230 --> 00:45:29,720 look at this one, the spread here, is much less 626 00:45:29,720 --> 00:45:34,120 than the other one. Even they have the same 627 00:45:34,120 --> 00:45:39,260 center, the same mean, but figure A is more spread 628 00:45:39,260 --> 00:45:45,140 than figure B. It means that the variation in A is 629 00:45:45,140 --> 00:45:49,920 much less than the variation in figure B. So it 630 00:45:49,920 --> 00:45:55,960 means that the mean is not sufficient to describe 631 00:45:55,960 --> 00:45:59,970 your data. Because maybe you have two datasets and 632 00:45:59,970 --> 00:46:03,330 both have the same mean, but the spread or the 633 00:46:03,330 --> 00:46:07,350 variation is completely different. Again, maybe we 634 00:46:07,350 --> 00:46:10,250 have two classes of statistics, class A and class 635 00:46:10,250 --> 00:46:13,230 B. The center or the mean or the average is the 636 00:46:13,230 --> 00:46:16,150 same for each one. For example, maybe the average 637 00:46:16,150 --> 00:46:19,810 of this class is 70. The average of class B is 638 00:46:19,810 --> 00:46:26,640 also 70. But the scores are scattered. or spread 639 00:46:26,640 --> 00:46:32,580 out in class A maybe much more than in class B. So 640 00:46:32,580 --> 00:46:34,280 the mean is not sufficient to describe the data. 641 00:46:34,360 --> 00:46:37,100 You have to say that the mean equals such and such 642 00:46:37,100 --> 00:46:41,000 and the spread. And one of these measures we'll 643 00:46:41,000 --> 00:46:44,500 talk later about range and variance standard 644 00:46:44,500 --> 00:46:49,030 deviation. So I mean, The mean by itself is not 645 00:46:49,030 --> 00:46:51,890 sufficient to describe the data. You have to use 646 00:46:51,890 --> 00:46:55,730 something else to measure the variation or the 647 00:46:55,730 --> 00:46:57,950 spread of the data. Make sense? 648 00:47:02,170 --> 00:47:05,670 The first measure of variation, the easiest one, 649 00:47:05,810 --> 00:47:11,230 is called the range. The range is the simplest 650 00:47:11,230 --> 00:47:15,590 measure of variation. The range is just the 651 00:47:15,590 --> 00:47:19,750 difference or the distance between the largest and 652 00:47:19,750 --> 00:47:23,550 the smallest value. For example, suppose the 653 00:47:23,550 --> 00:47:27,070 minimum score for this class is 40 and the maximum 654 00:47:27,070 --> 00:47:33,230 is 90. So the range is 50, 90 minus 40. Now 655 00:47:33,230 --> 00:47:38,850 imagine that the minimum score for this class is 656 00:47:38,850 --> 00:47:47,330 60 and the maximum is 80, so 20. If we replace 80 657 00:47:47,330 --> 00:47:51,450 by 100, I mean the minimum is 60 and the maximum 658 00:47:51,450 --> 00:47:57,030 is 100, it's 40. That means a range is affected by 659 00:47:57,030 --> 00:48:02,170 outliers because it depends only on two values. 660 00:48:03,480 --> 00:48:06,100 maximum and minimum value. So it should be 661 00:48:06,100 --> 00:48:09,320 affected by outliers. So range is sensitive to 662 00:48:09,320 --> 00:48:12,780 outliers. So if the data has the data set has 663 00:48:12,780 --> 00:48:15,660 outliers, then in this case, you have to avoid 664 00:48:15,660 --> 00:48:19,640 using range because range only based on two 665 00:48:19,640 --> 00:48:23,480 values. So it should be affected by outliers. Now 666 00:48:23,480 --> 00:48:25,880 for the for simple example, suppose we have this 667 00:48:25,880 --> 00:48:32,360 data. The minimum value is one. I mean, the 668 00:48:32,360 --> 00:48:34,680 smallest value is one, and the largest or the 669 00:48:34,680 --> 00:48:38,880 maximum is 13. So it makes sense that the range of 670 00:48:38,880 --> 00:48:41,840 the data is the difference between these two 671 00:48:41,840 --> 00:48:48,540 values. So 13 minus one is 12. Now, imagine that 672 00:48:48,540 --> 00:48:58,040 we just replace 13 by 100. So the new range will 673 00:48:58,040 --> 00:49:03,820 be equal to 100 minus 199. So the previous range 674 00:49:03,820 --> 00:49:08,340 was 12. It becomes now 99 after we replace the 675 00:49:08,340 --> 00:49:12,100 maximum by 100. So it means that range is affected 676 00:49:12,100 --> 00:49:18,740 by extreme values. So the mean and range both are 677 00:49:18,740 --> 00:49:23,040 sensitive to outliers. So you have to link between 678 00:49:26,410 --> 00:49:30,210 measures of center tendency and measures of 679 00:49:30,210 --> 00:49:33,130 variation. Mean and range are affected by 680 00:49:33,130 --> 00:49:37,910 outliers. The mean and range are affected by 681 00:49:37,910 --> 00:49:41,450 outliers. This is an example. So it's very easy to 682 00:49:41,450 --> 00:49:49,550 compute the mean. Next, if you look at why the 683 00:49:49,550 --> 00:49:51,190 range can be misleading. 684 00:49:53,830 --> 00:49:56,810 Sometimes you report the range and the range does 685 00:49:56,810 --> 00:50:00,310 not give an appropriate answer or appropriate 686 00:50:00,310 --> 00:50:04,450 result because number 687 00:50:04,450 --> 00:50:06,790 one ignores the way in which the data are 688 00:50:06,790 --> 00:50:10,770 distributed. For example, if you look at this 689 00:50:10,770 --> 00:50:15,430 specific data, we have data seven, eight, nine, 690 00:50:15,590 --> 00:50:18,110 ten, eleven and twelve. So the range is five. 691 00:50:19,270 --> 00:50:21,910 Twelve minus seven is five. Now if you look at the 692 00:50:21,910 --> 00:50:26,360 other data, The smallest value was seven. 693 00:50:29,600 --> 00:50:33,260 And there is a gap between the smallest and the 694 00:50:33,260 --> 00:50:38,220 next smallest value, which is 10. And also we have 695 00:50:38,220 --> 00:50:44,480 12 is repeated three times. Still the range is the 696 00:50:44,480 --> 00:50:48,140 same. Even there is a difference between these two 697 00:50:48,140 --> 00:50:53,640 values, between two sets. we have seven, eight, 698 00:50:53,760 --> 00:50:57,020 nine up to 12. And then the other data, we have 699 00:50:57,020 --> 00:51:02,180 seven, 10, 11, and 12 three times. Still, the 700 00:51:02,180 --> 00:51:06,360 range equals five. So it doesn't make sense to 701 00:51:06,360 --> 00:51:09,620 report the range as a measure of variation. 702 00:51:10,520 --> 00:51:12,640 Because if you look at the distribution for this 703 00:51:12,640 --> 00:51:15,500 data, it's completely different from the other 704 00:51:15,500 --> 00:51:20,860 dataset. Even though it has the same range. So 705 00:51:20,860 --> 00:51:25,220 range is not used in this case. Look at another 706 00:51:25,220 --> 00:51:25,680 example. 707 00:51:28,300 --> 00:51:32,920 We have data. All the data ranges, I mean, starts 708 00:51:32,920 --> 00:51:38,680 from 1 up to 5. So the range is 4. If we just 709 00:51:38,680 --> 00:51:46,200 replace the maximum, which is 5, by 120. So the 710 00:51:46,200 --> 00:51:49,190 range is completely different. the range becomes 711 00:51:49,190 --> 00:51:55,010 119. So that means range 712 00:51:55,010 --> 00:51:59,230 is sensitive to outliers. So we have to avoid 713 00:51:59,230 --> 00:52:06,030 using range in case of outliers or extreme values. 714 00:52:08,930 --> 00:52:14,410 I will stop at the most important one, the 715 00:52:14,410 --> 00:52:18,350 variance, for next time inshallah. Up to this 716 00:52:18,350 --> 00:52:19,310 point, any questions? 717 00:52:22,330 --> 00:52:29,730 Okay, stop at this point if 718 00:52:29,730 --> 00:52:30,510 you have any question. 719 00:52:35,430 --> 00:52:39,430 So later we'll discuss measures of variation and 720 00:52:39,430 --> 00:52:44,810 variance, standard deviation up to the end of this 721 00:52:44,810 --> 00:52:45,090 chapter. 722 00:52:54,630 --> 00:53:00,690 So again, the range is sensitive to outliers. So 723 00:53:00,690 --> 00:53:03,850 we have to avoid using range in this case. And 724 00:53:03,850 --> 00:53:06,270 later we'll talk about the variance, which is the 725 00:53:06,270 --> 00:53:09,750 most common measures of variation for next time, 726 00:53:09,830 --> 00:53:10,130 inshallah.