You will find the **Mean value from a frequency table** if you don’t know the exact values in the classes.

Suppose someone did a survey to find out how many cups of water people drink each day. The person who conducted the survey interviewed 52 people and gave them this frequency table to get the mean.

Since you don’t know the values in the classes, you can pretend that each value in a class is estimated by the class center point.

For example, the possible values in Class 4-6 are 4, 5, and 6.

Since you have no idea how often 4, 5, or 6 appear in this class, just use the class midpoint or 5.

Note that the frequency of this class is 15. This means that the raw data for classes 4-6 “specify”

5 5 5 5 5

5 5 5 5 5

5 5 5 5 5

The ” **pretend** “Raw data for grades 1-3 are

2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2

The ” **pretend** “Raw data for grades 7-9 are

8 8 8 8 8

8 8 8 8 8

The ” **pretend** “Raw data for grades 10-12 are

11 11 11 11 11

The ” **pretend** “Raw data for grades 13-15 are

14 14

There are 52 numbers from these 5 classes.

To find the mean, you need to add those 52 numbers and divide by 52.

Instead of adding 52 numbers, there is an easier way

You can do 15 × 5 + 20 × 2 + 10 × 8 + 5 × 11 + 2 × 14

The above math is found by multiplying the **frequency** and the **Class center** and then add the totals.

## Formula to use to get the mean of a frequency table

If f is the frequencies and x is the midpoints, the math can be expressed as Σ f × x

To get 52 you need to add the frequencies. This can be expressed as Σ f

Use the following formula to get the mean from a frequency table:

Using our table above, we can calculate the mean values shown below:

Mean =

15 × 5 + 20 × 2 + 10 × 8 + 5 × 11 + 2 × 14

52

Mean =

75 + 40 + 80 + 55 + 28

52

Mean = 5.346

We can therefore conclude that people drink an average of 5.346 cups of water every day.