# Find Mode, Median and Range from Frequency Tables

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

Key stage:  KS 3

Curriculum topic:   Statistics

Curriculum subtopic:   Understand Variables, Representation, Measures and Spread

Difficulty level:

#### Worksheet Overview

How could you organise the following data on the number of pets owned by children in a Year 8 class?

We could use a frequency table!

Number of pets 0 1 2
Frequency 11 14 5

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

This means that:

11 children have no pets

14 children have one pet

5 children have two pets

Data organised in a frequency table can be used to work out the median, mode and range (as well as mean - but that is not our focus today!).

Median

There are 11 + 14 + 5 = 30 children, so the 'middle person' will be the (30 + 1) ÷ 2 = 15.5th person, i.e. the number that would be between the 15th and 16th!

The 15th and 16th person both fall into the second category.

This is because there are 11 people in the first one and 14 in the second one, so the second category is 12th to 11 + 14 = 26th person.

The second category people have 1 pet so the median number of pets is 1.

Mode

This is the one with the highest frequency.

Most children (14) have 1 pet.

So the modal number of pets is 1!

That was easy!

Range

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

Range is therefore: 2 - 0 = 2

Be careful that it's always the data we are collecting, not the frequency, that will be the final answer!