Let us find the mean of the following data.

The arithmetic mean is also called average or average value, is the sum of the data or variables divided by total number of data or variables.

This is an inclusive type of data, so in order to find the average or arithmetic mean we need to convert it into exclusive type of data.

To convert inclusive type of data into exclusive type, subtract 0.5 from the lower class limit and add 0.5 to upper class limit.

For example, in class limit 5 – 14:

Subtract 0.5 from lower class limit and add 0.5 to upper class limit.

5 – 0.5 = 4.5

14 + 0.5 = 14.5

So, the class interval comes out to be 4.5 – 14.5.

Similarly, we have with other class intervals.

Let’s make a table showing exclusive type of data.

So, we have

∑f_ix_i = 2140

∑f_i = 60

From direct method, mean is given by

Using the above values,

⇒ Mean = 35.67

Thus, mean is 35.67.