Question

The mean of the following distribution is $18$. Find the frequency f of the class $19-21$.

Class	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Frequency	$3$	$6$	$9$	$13$	$f$	$5$	$4$

Answer 1

Class Interval	Mid Value $x_i$	Frequency $f_i$	$f_i{x}_i$
11 - 13	12	3	36
13 - 15	14	6	84
15 - 17	16	9	144
17 - 19	18	13	234
19 - 21	20	$f$	20 $f$
21 - 23	22	5	110
23 - 25	24	4	6
		$\sum f=40+f$	$\sum fx=704+20f$

Given : Mean $=18$

We know, Mean $\left(\overline{x}\right)=\frac{\Sigma fx}{\Sigma f}$

$⟹18=\frac{704+20f}{40+f}$

$⟹18(40+f)=704+20f$

$⟹720+18f=704+20f$

$⟹720-704=20f-18f$

$⟹2f=16$

$⟹f=8$