If the mean of the following data is 15, find p.

Solution:

Given:

Also, mean = 15

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

$15=\frac{445+10 p}{27+p}$

By using cross multiplication method

$405+15 p=445+10 p$

$15 p-10 p=445-405$

$5 p=40$

$p=\frac{40}{5}$

$=8$

Hence, $p=8$