Question

Find the mean of following distribution with step-deviation method to the nearest integer

Class	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40
Frequency	5	6	8	12	6	3

Answer 1

Class	$x_i$	$f_i$	Let A = $U_i=\frac{x_i-27.5}{5}$	$f_i{u}_i$
10 - 15	12.5	5	-3	-15
15 - 20	17.5	6	-2	-12
20 - 25	22.5	8	-1	-8
25 - 30	27.5	12	0	0
30 - 35	32.5	6	1	6
35 - 40	37.5	3	2	6
		$\sum f_i=40$		$\sum f_i{u}_i=-23$

$\Rightarrow \overline{x}=A+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)h\Rightarrow \overline{x}=27.5+5\times \left(\frac{-23}{40}\right)=24.625$