Find the missing value of $p$ for the following distribution whose mean is 12.58.

$x$	5	8	10	12	$p$	20	25
$f$	2	5	8	22	7	4	2

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Given:

The mean of the given data is 12.58.

To do:

We have to find the value of $p$.

Solution:

We know that,  

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

Therefore,

Mean $12.58=\frac{524+7p}{50}$

$12.58(50)=524+7p$

$629=524+7p$

$7p=629-524$

$p=\frac{105}{7}$

$p=15$