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Question

Calculate standard deviation of the following data, using step-deviation method.
Age 20−30 30−40 40−50 50−60 60−70 70−80 80−90
Frequency 3 61 132 153 140 51 2

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Solution

Age
Mid value
m

Frequency
(f)

Deviation assumed from average
(dx = m − A)
dx'=dxc=dx10 fdx'=f×dx' fdx'2=f×dx'2
20−30
30 −40
40 −50
50 −60
60 −70
70 −80
80 −90
25
35
45
55=A
65
75
85
3
61
132
153
140
51
2
−30
−20
−10
0
10
20
30
−3
−2
−1
0
1
2
3
−9
−122
−132
0
140
102
6
27
244
132
0
140
204
18
N = 542 Σfdx' = -15 Σfdx'2 = 765

Standard deviation (σ)=Σfdx'2N-Σfdx'N2×cor, σ =765542--155422×10or, σ =1.41--0.032×10or, σ =1.41-0.0009×10or, σ =1.19×10 σ =11.9

Hence, standard deviation of the above data is 11.9

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