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Find the Mode

In this worksheet, students practise finding the mode of a distribution.

'Find the Mode' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Analysing Data

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

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

1,2,3,4,5,6,7,8,9

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

Red

Blue

Green

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?

Blue

Green

Brown

Other

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

1 < p < 2

2 < p < 3

3 < p < 4

4 < p < 5

Complete the sentence...

0 < p < 1

1 < p < 2

2 < p < 3

3 < p < 4

4 < p < 5

  • Question 1

We find the mode by looking for the value that has....

CORRECT ANSWER
EDDIE SAYS
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.
  • Question 2

Find the mode for 7,8,3,6,7,3,8,5,4,9,7

CORRECT ANSWER
EDDIE SAYS
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.
  • Question 3

4,8,7,5,9,4,8,3,3

 

Does this data have...

CORRECT ANSWER
It is bimodal
EDDIE SAYS
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)
  • Question 4

1,2,3,4,5,6,7,8,9

Does this data have...

CORRECT ANSWER
It has no mode
EDDIE SAYS
Nothing appears more than anything else. This tells us the data has ...
  • Question 5

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

CORRECT ANSWER
1
EDDIE SAYS
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.
  • Question 6

Find the modal category

Red, Green, Blue, Red, Red, Blue, Green, Blue, Red

CORRECT ANSWER
Red
EDDIE SAYS
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.
  • Question 7

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?

CORRECT ANSWER
7
EDDIE SAYS
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.
  • Question 8

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?

CORRECT ANSWER
Brown
EDDIE SAYS
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...
  • Question 9

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

 

CORRECT ANSWER
4 < p < 5
EDDIE SAYS
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...
  • Question 10

Complete the sentence...

CORRECT ANSWER
EDDIE SAYS
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!
---- OR ----

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