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The following table shows frequency distribution of some data

Class
0-20
20-40
40-60
60-80
80-100
100-120
120-140
Frequency
6
8
10
12
6
5
3

The mean using step-deviation method will be ____.

see full answer

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Detailed Solution

The mean using step-deviation method will be 62.4.
Given:

Class	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency	6	8	10	12	6	5	3

Formula:

Mean = A + ∑ f i d i ∑ f i

, where

A

is the assumed mean,

f

is the frequency and

d

is the mean deviation of the given data.
We have to find the mean of the following frequency distribution using the step-deviation method. Let

A = 70

be the assumed mean. The frequency and deviation table will be

Class	Frequency (fi)	Mid-value (xi)	Deviation, di=xi-A	fidi
0-20	6	10	-60	-360
20-40	8	30	-40	-320
40-60	10	50	-20	-200
60-80	12	70=A	0	0
80-100	6	90	20	120
100-120	5	110	40	200
120-140	3	130	60	180
	Σfi=50			Σfidi=-380

Observing from the above table:

A = 70, ∑ f i = 50, ∑ f i d i = − 380

Substituting the values in formula:

M e a n = 70 + − 380 50 M e a n = 70 − 7.6 M e a n = 62.4

Hence, the mean of the given data is 62.4.
The mean of the frequency distribution using step-deviation method is 62.4.

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