Question

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

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

$\Rightarrow$ $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$

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

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

$\Rightarrow$ $21=3P$
$\Rightarrow p=\frac{21}{3}$

$\therefore$ $P=7$