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	30	16	10

Answer 1

Let the assumed mean A = 25

Marks	Mid-value x	f	d = x – A	`bb(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