Question

Find the mean of the following frequency distribution using step-deviation method.

Take assumed mean = 28

Class Interval	0 − 8	8 − 16	16 − 24	24 − 32	32 − 40	40 − 48
Frequency	10	20	14	16	18	22

Answer 1

Given: i = class size = 8 and assumed mean (A) = 28

Class Interval	Frequency (f)	Class mark (x)	d = x − A	t = `(x − A)/i`	ft
0 − 8	10	4	−24	−3	−30
8 − 16	20	12	−16	−2	−40
16 − 24	14	20	−8	−1	−14
24 − 32	16	28	0	0	0
32 − 40	18	36	8	1	18
40 − 48	22	44	16	2	44
Total	`sumf = 100`				`sumft= -22`

By formula,

Mean = `A + (sum ft)/(sumf) xx i`

= `28 + (-22/100) xx 8`

= 28 + 8(−0.22)

= 28 − 1.76

= 26.24