Averages from Frequency Charts

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.

 

Example

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

Find the mean, median and mode.

 

 

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.

 

Mean

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

 

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) = 2910 cm

 

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

 

Mean height = 2910 ÷ 22 = 132.3 cm (1 dp)

 

Median

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 135cm.

 

Mode

This is the class with the highest frequency.

The modal class  130 cm to 135cm.