Question

If the mean of the following data is 15,

$x_i$	6	P	6	10	5
$f_i$	5	10	15	20	25

then the value of P is

• A. 28
• B. 38
• C. 68
• D. 78

Answer 1

The correct option is C 68

$x_i$	$f_i$	$f_i{x}_i$
6	5	30
P	10	10P
6	15	90
10	20	200
5	25	125
	${\sum }_{i=1}^5{f}_i=75$	${\sum }_{i=1}^5{f}_i{X}_i=445+10P$

Mean, $\overline{x}=\frac{{\sum }_{i=1}^5{f}_1}{{\sum }_{i=1}^5{f}_i{X}_i}$

$\Rightarrow 15=\frac{445+10P}{75}$

$\Rightarrow 15\times 75=445+10P$
$\Rightarrow 1125=445+10P$
$\Rightarrow 1125-445=10P$
$\Rightarrow 680=10P$
$\Rightarrow P=68$
Hence the correct answer is option c.