Find the value of $p$, if the mean of the following distribution is 20.

$x$	15	17	19	$20+p$	23
$f$	2	3	4	$5p$	6

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The arithmetic mean of the given data is 20.

To do:

We have to find the value of $p$.

Solution:

 We know that,

Mean$=\frac{\sum fx}{\sum f}$ 

Mean $20=\frac{295+100p+5p^2}{15+5p}$ 

$20(15+5p)=295+100p+5p^2$

$5p^2+100p+295=100p+300$

$5p^2=300-295$

$5p^2=5$

$p^2=1$

$p=1$