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Question

Calculate standard deviation of the following series:
Size 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40
Frequency 2 5 7 13 21 16 8 3

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Solution

Size
Mid Value
m

Frequency Deviation from assumed Average
(dx = m − A)
dx'=dxC C=5
fdx' fdx'2
0 − 5
5 − 10
10 − 15
15 − 20
20 − 25
25 − 30
30 − 35
35 − 40
2.5
7.5
12.5
17.5(A)
22.5
27.5
32.5
37.5
2
5
7
13
21
16
8
3
−15
−10
−5
0
5
10
15
20
−3
−2
−1
0
1
2
3
4

−6
−10
−7
0
21
32
24
12
18
20
7
0
21
64
72
48
N = 75 Σfdx' = 66 Σfdx'2 = 250

Calculating Standard deviation through Step deviation method:

Standard deviation (σ )=Σfdx'2N-Σfdx'N2×Cor, σ=Σfdx'2N-Σfdx'N2×5or, σ =25075-66752×5or, σ =3.33-0.7744 ×5or, σ =2.5556×5or, σ =1.598×5 σ =7.99

Hence, standard deviation of the above series is 7.99.

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