Question

Find the mean of the following frequency distribution by the step deviation method : 

Class	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency	12	24	52	88	66	42	16

Answer 1

Class Interval	xi	fi	A = 70 ${\displaystyle \text{u}=\frac{\text{x - A}}{{\text{h}}_i}}$	${\displaystyle f_{i}u}$
0-20	10	12	-3	-36
20-40	30	24	-2	-48
40-60	50	52	-1	-52
60-80	A = 70	88	0	0
80-100	90	66	1	66
100-120	110	42	2	84
120-140	130	16	3	48
Total		300		62

A= 70 and h_i = 20 

${\displaystyle \overline{x}=\text{A}+\text{h}\times \frac{\Sigma f_i\text{u}}{\Sigma f_i}}$

${\displaystyle \overline{x}=70+20\times \frac{62}{300}}$

${\displaystyle \overline{x}=70+4.13}$

${\displaystyle \overline{x}=74.13}$

∴ Mean = 74.13