The following table gives the number of boys of a particular age in a class of 40 students.
Question:

The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students

Solution:

Given:

First of all prepare the frequency table in such a way that its first column consist of the values of the variate $\left(x_{i}\right)$ and the second column the corresponding frequencies $\left(f_{i}\right)$.

Thereafter multiply the frequency of each row with corresponding values of variable to obtain third column containing $\left(f_{i} x_{i}\right)$.

Then, sum of all entries in the column second and denoted by $\sum f_{i}$ and in the third column to obtain $\sum f_{i} x_{i}$.

We know that mean, $\bar{X}=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$\bar{X}=\frac{698}{40}$

$=17.45$

Hence, the mean age of the students $=17.45$ years