Question

If the arithmetic mean of following data is 17, find the value of P.

Term(x)	10	15	20	25
Frequency(f)	7	10	P	6

Answer 1

$Term\left(x_i\right)$	$Frequency$ $\left(f_i\right)$	$f_i{x}_i$
$10$	$7$	$70$
$15$	$10$	$150$
$20$	$P$	$20P$
$25$	$6$	$150$
	$\sum f_i=23+P$	$\sum f_i{x}_i=370+20P$

We know that, $Mean=\frac{\sum f_i{x}_i}{\sum f_i}$

$\Rightarrow$ $17=\frac{370+20P}{23+P}$

$\Rightarrow$ $391+17P=370+20P$

$\Rightarrow$ $3P=21$

$\therefore$ $P=7$

Hence, the value of $P$ is $7$.