Question

Find the arithmetic mean (correct to the nearest whole number) by using step-deviation method.

x	5	10	15	20	25	30	35	40	45	50
f	20	43	75	67	72	45	39	9	8	6

Answer 1

Let the assumed mean = 30

x	f	d = x – A A = 30	`bb(t = (x - A)/i` `bb(= (x - 30)/5)`	ft
5	20	–25	–5	–100
10	43	–20	–4	–172
15	75	–15	–3	–225
20	67	–10	–2	–134
25	72	–5	–1	–72
30	45	0	0	0
35	39	5	1	39
40	9	10	2	18
45	8	15	3	24
50	6	20	4	24
	Σf = 384			Σft = –598

By step deviation method, we have

Mean = `A + (Σft)/(Σf) xx i`

= `(30 + (598) xx 5)/384`

= `30 + (-598)/384 xx 5`

= 30 – 7.79

= 22.21

= 22 (appx.) [To nearest whole number]