# Find the Mean From a Frequency Table

In this worksheet, students will find the mean from a frequency table.

Key stage:  KS 3

Curriculum topic:   Statistics

Curriculum subtopic:   Understand Variables, Representation, Measures and Spread

Difficulty level:

#### Worksheet Overview

What is frequency?

In physics, you might have heard of the frequency of sound.

In maths, frequency is much simpler - it's just the number of times something occurs!

For example, below we have the frequency table made from responses to a survey on the number of pets owned:

 Number of pets 0 1 2 3 4 Frequency 7 6 5 2 1

We can see that 0 pets has the frequency of 7, so 7 people responded with '0 pets owned'.

We can find the mean from a frequency table just as we do if we have the data points in a list:

mean = sum of all data points ÷  number of data points

The total number of people here, i.e. the number of data points, is all the frequencies added together:

7 + 6 + 5 + 2 + 1 = 21

From the table, we have:

7 people have 0 pets which is a total of 7 x 0 = 0 pets

6 people have 1 pet which is a total of 6 x 1 = 6 pets

5 people have 2 pets which is a total of 5 x 2 = 10 pets

2 people have 3 pets which is a total of 2 x 3 = 6 pets

1 person has 4 pets which is a total of 1 x 4 = 4 pets

So altogether, we get the total number of pets, i.e sum of all data points, is:

0 + 6 + 10 + 6 + 4 = 26 pets

Mean number of pets = the total number of pets ÷ the total number of people

The mean number of pets is  26 ÷  21 = 1.2 pets per person.