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 $f$.

Daily pocket allowance (in $Rs.$)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Number of children	$3$	$6$	$9$	$13$	$k$	$5$	$4$

Answer 1

$xi$ (mid point of class)	frequency $fi$	$fixi$
$12$	$3$	$36$
$14$	$6$	$84$
$16$	$9$	$144$
$18$	$13$	$234$
$20$	$k$	$20k$
$22$	$5$	$110$
$24$	$4$	$96$
	$\sum =k+240$	$\sum 704+20k$

mean $=\frac{\sum fixi}{\sum fi}=\frac{20k+704}{k+40}\Rightarrow 20k+704=18k+720$

$\Rightarrow 2k=16$

$\Rightarrow k=8$