Question

Find the missing value of P for the following distribution whose mean is 12.58

x	5	8	10	12	P	20	25
y	2	5	8	22	7	4	2

Answer 1

Given $\overline{x}=12.58$

$x_i$	$f_i$	$f_i{x}_i$
5	2	10
8	5	40
10	8	80
12	22	264
P	7	7P
20	4	80
25	2	50
	$f_i=50$	$f_i{x}_i=524+7P$

$\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$
$\Rightarrow 12.58=\frac{524+7P}{50}\Rightarrow 629=524+7P$
$\Rightarrow 7P=105$
$\Rightarrow P=15$