If the mean of the following distribution is 27, find the value of $p$.

Class:	0-8	10-20	20-30	30-40	40-50
Frequency:	8	$p$	12	13	10

Given:

The mean of the given distribution is 27.

To do:

We have to find the value of $p$.

Solution:

Mean $=27$

 We know that,

Mean $=\frac{\sum{f_ix_i}}{\sum{f_i}}$    

Therefore,  

Mean $27=\frac{1245+15p}{43+p}$

$27(43+p)=1245+15p$                  

$1161+27p=1245+15p$

$1245-1161=27p-15p$

$p=\frac{84}{12}$

$p=7$

The value of $p$ is $7$.