Mathematics

Find the arithmetic mean (correct to nearest whole number) by using step deviation method.
x f
5 20
10 43
15 75
20 67
25 72
30 45
35 39
40 9
45 8
50 6

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Let assumed mean (A) be 25.

x	f	d = x - A	t = (x - A)/i	ft
5	20	-20	-4	-80
10	43	-15	-3	-129
15	75	-10	-2	-150
20	67	-5	-1	-67
A = 25	72	0	0	0
30	45	5	1	45
35	39	10	2	78
40	9	15	3	27
45	8	20	4	32
50	6	25	5	30
Total	Σf = 384			Σft = -214

By formula,

Mean = A + $\dfrac{Σft}{Σf} \times i = 25 + \dfrac{-214}{384} \times 5$

= 25 - $\dfrac{1070}{384}$

= 25 - 2.786

= 22.21 ≈ 22.

Hence, mean = 22.

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