Question

Calculate the arithmetic mean for the following data using step deviation method.

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
No. of students	$8$	$15$	$22$	$20$	$10$	$5$

Answer 1

Marks	Midpoint($x_i$)	No. of students($f_i$)	Deviation($d_i$)	$u_i$	$u_i{f}_i$
0-10	5	8	-30	-3	-24
10-20	15	15	-20	-2	-30
20-30	25	22	-10	-1	-22
30-40	35	20	0	0	0
40-50	45	10	10	1	10
50-60	55	5	20	2	10

N=$\sum f_i=80$, h=$10$

A=$35$,$d_i=x_i-A$ , $u_i=\frac{d_i}{h}$

Mean=$A+h\left(\frac{\sum u_i{f}_i}{N}\right)=35+10\left(\frac{-56}{80}\right)$

Mean=$28$