Question

The following distribution shows the daily pocket allowance given the children of a multistorey building. The average pocket allowance is Rs. $18.00$. Find out the missing frequency.

Class interval:	11-13	13-15	15-17	17-19	19-21	21-23	23-25
Frequency:	$7$	$6$	$9$	$13$	---	$5$	$4$

Answer 1

Answer:-

Let the missing frequency be $x$.

Class interval	Frequency	$x_i$	$f_i{x}_i$
11-13	7	12	84
13-15	6	14	84
15-17	9	16	144
17-19	13	18	234
19-21	$x$	20	20$x$
21-23	5	22	110
23-25	4	24	96
	$\Sigma f_i=44+x$		$\Sigma f_i{x}_i=752+20x$

$\text{average pocket allowance}\overline{x}=\frac{\Sigma f_i{x}_i}{\Sigma f_i}=18\Rightarrow \left(given\right)$

$\therefore \frac{752+20x}{44+x}=18$

$\Rightarrow 752+20x=18(44+x)$

$\Rightarrow 752+20x=792+18x$

$\Rightarrow 2x=40$

$\Rightarrow x=20$

Hence, the missing frequency is $20$.