Question

The mean of the following frequency distribution is $16$, find the missing frequency

Class	0-4	4-8	8-12	12-16	16-20	20-24	24-28	28-32	32-36
Frequency	6	8	17	23	16	15	-	4	3

Answer 1

$\Rightarrow$ $\overline{x}=16$ [ Given ]

$Class$	$Frequency$ $f_i$	$Mid-value$ $x_i$	$f_i{x}_i$
$0-4$	$6$	$2$	$12$
$4-8$	$8$	$6$	$48$
$8-12$	$17$	$10$	$170$
$12-16$	$23$	$14$	$322$
$16-20$	$16$	$18$	$288$
$20-24$	$15$	$22$	$330$
$24-28$	$x$	$26$	$26x$
$28-32$	$4$	$30$	$120$
$32-36$	$3$	$34$	$102$
	$\sum f_i=92+x$		$\sum f_i{x}_i=1392+26x$

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

$\Rightarrow$ $16=\frac{1392+26x}{92+x}$

$\Rightarrow$ $1472+16x=1392+26x$

$\Rightarrow$ $10x=80$

$\therefore$ $x=8$

$\Rightarrow$ The missing frequency is $8$.