Find Averages from Frequency Tables

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

 

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.

 

Example

This table shows the number of pets owned by children in a Year 8 class at school.

Find the mean, median, mode and range.

 

Number of pets	0	1	2
Frequency	11	14	5

 

This means that:

11 children have no pets

14 children have one pet

 5 children have two pets

  

Mean

There are (11 x 0) + (14 x 1) + (5 x 2) = 0 + 14 + 10 = 24 pets in total.

There are 11 + 14 + 5 = 30 children in the class.

 

Mean number of pets = 24 ÷ 30 = 0.8

 

Median

There are 30 children, so the 'middle person' will be the 15th and 16th.

The 15th and 16th person both fall into the middle category and have 1 pet.

The median number of pets is 1

 

Mode

This is the one with the highest frequency.

Most children (14) have 1 pet.

The modal number of pets is 1

 

Range

The largest number of pets is 2 and the smallest is 0.

Range = 2 - 0 = 2

 

Does that make sense?

 

Let's get started!