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Find Averages from Frequency Charts

In this worksheet, students will read grouped data from frequency charts in order to work out the mean, median and mode.

'Find Averages from Frequency Charts' worksheet

Key stage:  KS 3

Year:  Year 8 Maths worksheets

Curriculum topic:   Statistics

Curriculum subtopic:   Understand Variables, Representation, Measures and Spread

Difficulty level:  

Worksheet Overview

Data organised in a frequency chart can be used to work out the mean, median and mode.


The number of items in the group can be found by adding up the frequencies.  

Remember that 'frequency' is just 'how many times' something occurs.


When data is grouped, the exact value is not known.



This chart shows the heights of children in a Year 6 class at school.

Find the mean, median and mode.


bar chart to show heights of a class of children


This means that:

0 children have a height between 110 cm and 115 cm.

1 child has a height between 115 cm and 120 cm.

3 children have a height between 120 cm and 125 cm ..... etc.



We have to estimate the mean by using the midpoint value in each class.

These are 112.5, 117.5, 122.5, 127.5, 132.5, 137.5, 142.5, 147.5 and 152.5 cm


We multiply these midpoint values by the frequency that they occur. eg. 3 x 122.5 because three children are in that height group.


The total estimated height of all the children is    (1 x 117.5) + (3 x 122.5) + (4 x 127.5) + (7 x 132.5) + (4 x 137.5) + (2 x 142.5) + (1 x 152.5) = 2,910 cm


There are 1 + 3 + 4 + 7 + 4 + 2 + 1 = 22 children in the class.


Mean height = 2,910 ÷ 22 = 132.3 cm (1 dp)



There are 22 children, so the 'middle person' will be the 11th and 12th.

The 11th and 12th people fall into the 130 cm to 135 cm class.

The median class is 130 cm to 135 cm.



This is the class with the highest frequency.

The modal class is 130 cm to 135 cm.


That's a lot of information to take in - don't worry if you can't remember it all, you can check back to this introduction at any point during the activity by clicking on the red button on the side of the screen.


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