Question

The following distribution shows the daily pocket allowance of children of a locality . The mean pocket allowance is $Rs.18.$ Find the missing frequency $f$ ?

Dally pocket allowance (in Rs)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

Answer 1

$Dailypocketallowance(inRs.)$	$Mid-value$ $x_i$	$No.ofchildren$ $f_i$	$f_i{x}_i$
$11-13$	$12$	$7$	$84$
$13-15$	$14$	$6$	$84$
$15-17$	$16$	$9$	$144$
$17-19$	$18$	$13$	$234$
$19-21$	$20$	$f$	$20f$
$21-23$	$22$	$5$	$110$
$23-25$	$24$	$4$	$96$
		$\sum f_i=44+f$	$\sum f_i{x}_i$ $=752+20f$

$\Rightarrow$ $\overline{x}=18$ [ Given ]

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

$\Rightarrow$ $18=\frac{752+20f}{44+f}$

$\Rightarrow$ $18=\frac{2(376+10f)}{44+f}$

$\Rightarrow$ $9=\frac{376+10f}{44+f}$

$\Rightarrow$ $396+9f=376+10f$

$\therefore$ $f=20$