Question

Helping the step deviation method find the arithmetic mean of the distribution:

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

Answer 1

Let the assumed Mean be A = 25 and h = 5.

`x_i`	Frequencies `f_i`	Deviation `d_i = x_i - 25`	`u_i = (x_i - 25)/(5)`	`f_iu_i`
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
	N = `sum_i = 384`			`sumf_iu_i = -214`

We have,
N = 384, A = 25, h = 5 and `sumf_iu_i = -214`
Mean `bar"(X)" = "A" + "h" (1/"N" sumf_iu_i)`
= `25 + 5 xx ((-214)/(384))`
= 25 - 2·786
= 22·214.