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 c)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-35$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

Answer 1

To determine the missing frequency, we will use the mean formula.

Here, mean $=\overline{x}=18$

Class interval	Number of children ($f_i$)	Class-mark ($x_i$)	$f_i{x}_i$
$11-13$	$7$	$12$	$84$
$13-15$	$6$	$14$	$84$
$15-17$	$9$	$16$	$144$
$17-19$	$13$	$18=A$	$234$
$19-21$	$f$	$20$	$20f$
$21-23$	$5$	$22$	$110$
$23-35$	$4$	$24$	$96$
Total	$\sum f_i=44+f$		$\sum f_i{x}_i=752+20f$

Formula

The mean formula is

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

$$\begin{gathered} 18=\frac{(752+20f)}{(44+f)} \\ \Rightarrow 18(44+f)=(752+20f) \\ \Rightarrow 792+18f=752+20f \\ \Rightarrow 792+18f=752+20f \\ \Rightarrow 792–752=20f–18f \\ \Rightarrow 40=2f \\ \Rightarrow f=20 \end{gathered}$$

Hence, the missing frequency,$f=20.$