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.)	Number of children
11-13	7
13-15	6
15-17	9
17-19	13
19-21	f
21-23	5
23-25	4

• A. $f=10$
• B. $f=20$
• C. $f=15$
• D. $f=19$

Answer 1

The correct option is B $f=20$

Answer:- $x_i=\frac{\text{lower limit + upper limit}}{2}$

Daily pocket allowance (in Rs.)	$x_i$	$f_i$	$x_i{f}_i$
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
		$\Sigma f_i=44+f$	$\Sigma x_i{f}_i=752+20f$

$\therefore Mean=\frac{\Sigma x_i{f}_i}{\Sigma f_i}=\frac{752+20f}{44+f}$

Given:- Mean $=18$

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

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

$\Rightarrow$ $2f=40$

$\Rightarrow$ $f=20$