If the mean of the following data is 20.6. Find the value of p.

Solution:

Given:

Also, mean $=20.6$

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, $\bar{X}=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$20.6=\frac{530+25 p}{50}$

By using cross multiplication method,

$530+25 p=20.6 \times 50$

$25 p=1030-530$

$p=\frac{500}{25}$

$=20$

Hence, $p=20$