Question

Calculate the mean of the following distribution using step deviation method.

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of students	10	9	25	0	16	10

Answer 1

Let the assumed mean A = 25

Marks	Mid-value x	f	d = x - A	`t= (x-A)/i = (x-25)/10`	ft
0 - 10	5	10	-20	-2	-20
10 - 20	15	9	-10	-1	-9
20 - 30	25	25	0	0	0
30 - 40	35	30	10	1	30
40 - 50	45	16	20	2	32
50 - 60	55	10	30	3	30
		`sumf= 100`			`sumft = 63`

`:. Mean = A+ (sumft)/(sumf) xx i = 25 + 63/100 xx 10 = 25 + 63/10 = 25 + 6.3 = 31.3`