Find the Mode
In this worksheet, students practise finding the mode of a distribution.
GCSE Subjects: Maths
GCSE Boards: AQA, Eduqas, Pearson Edexcel, OCR
Curriculum topic: Statistics
Curriculum subtopic: Statistics, Analysing Data
The mode is the average that is probably the easiest to find but surprisingly, also the one that people get wrong the most.
This is because, in certain situations, it doesn't exist.
What is the mode:
The definition of mode is 'The value that has the highest frequency'
In reality, for a small data set, all we have to do is to find the number that is in the list most often.
How do we find the mode?
Simple, just count up the times something appears in the list, if it's there more than anything else, it's the mode.
Example 1: Find the mode for 2 1 4 2 5 5 6 8 5 5 7
There is one number that appears more than anything else.
The mode is 5
Example 2: Find the mode for 4 5 8 7 9 1 6 2 3
In this list, there isn't a single number that appears more than anything else
This means this data has no mode
Example 3: Find the modes for 4 5 9 9 7 6 4 4 2 9 5
In this data, there are 3 fours and 3 nines.
Technically, this means the data doesn't have a mode as one value doesn't appear more than anything else.
What is normally said is that the mode is both 4 and 9. This is called Bimodal data.
We find the mode by looking for the value that has....
Find the mode for 7,8,3,6,7,3,8,5,4,9,7
4,8,7,5,9,4,8,3,3
Does this data have...
It has a mode
It is bimodal
It has no mode
Find the mode for 3 1 5 5 1 3 1 5 1 3 1 1 5 1 3 1 5 1 1 1 5 1 3 1
Find the modal category
Red, Green, Blue, Red, Red, Blue, Green, Blue, Red
These are the results of a quick 10 mark test for a group of students
Mark 3 4 5 6 7 8 9 10
Frequency 2 1 3 3 8 2 1 1
What is the modal mark for this test?
We complete a survey about eye colours for our friends and put the data in a table
Colour Blue Green Brown Other
Frequency 6 2 11 4
What is the modal eye colour?
What is the modal class for this data?
Pocket Money (£p) 0 < p < 1 1 < p < 2 2 < p < 3 3 < p < 4 4 < p < 5
No of students 2 5 5 9 15
0 < p < 1
Complete the sentence...
Im going to be really picky here. Saying most often only works in a list, it doesn't work in anything else. We should always use the phrase highest frequency.
We are just looking for the number that is there more than anything else, that appears with the highest frequency. We can see the number 7 occurs more than any other number.
Two numbers appear more than any others (3 and 8). This means we have two modes (the Latin for two is Bi-, think of bicycle)
Nothing appears more than anything else. This tells us the data has ...
It\'s harder to spot straight away when it\'s only a few numbers repeated. We can count these and see that there are 13 number ones.
This is the thing the mode is best for. If there aren't numbers we can't use the mean or median so we have to use the mode Does it matter that it says modal category? Not in the slightest, we're still looking for the one that appears the most.
This is where the definition comes in. We said the mode was the value with the highest frequency. In this table, the mark that has the highest frequency is 7 marks out of 10. The modal mark would be 7.
Again, let's go down to the definition. 'The mode is the value with the highest frequency' The colour that has the biggest frequency is...
Again, we're playing around with the word mode. Modal class just means which group has the highest frequency. With a frequency of 15, the modal class is...
As I said at the very start, all the averages have advantages and disadvantages, the mode is great if you are dealing with non-numerical data but can be rubbish as it sometimes doesn\'t even exist!
Box Plots
Draw and Use a Line of Best Fit
Draw Cumulative Frequency Diagra...
Draw Histograms
Draw Pie Charts
Explain Median from a Frequency ...
Explain Time Series Data
Find Quartiles from a Distributi...
Find the Mean