Find the mean of the following frequency distribution using step-deviation method.
Take assumed mean = 28
Class interval Frequency
0 - 8 10
8 - 16 20
16 - 24 14
24 - 32 16
32 - 40 18
40 - 48 22
Measures of Central Tendency
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Question

Find the mean of the following frequency distribution using step-deviation method.
Take assumed mean = 28
Class interval Frequency
0 - 8 10
8 - 16 20
16 - 24 14
24 - 32 16
32 - 40 18
40 - 48 22

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KnowledgeBoat · Accepted Answer

Here, 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	∑f = 100				∑ft = -22

By formula,

Mean = $A + \Big(\dfrac{\sum ft}{\sum f} \Big) \times i$

= 28 + $\Big(-\dfrac{22}{100}\Big) \times 8$

= 28 + 8(-0.22)

= 28 - 1.76

= 26.24

Hence, mean = 26.24