Find the value of $p$ for the following distribution whose mean is 16.6.

$x$:	8	12	15	$p$	20	25	30
$f$:	12	16	20	24	16	8	4.

Given:

The mean of the given data is 16.6.

To do:

We have to find the value of $p$.

Solution:

We know that, 

Mean$=\frac{\sum fx}{\sum f}$

Therefore,

Mean $16.6=\frac{1228+24p}{100}$

$16.6(100)=1228+24p$

$1660=1228+24p$

$24p=1660-1228$

$p=\frac{432}{24}$

$p=18$