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Question

Calculate mean and standard deviation of the following data by short-cut method:
Class Interval 10−20 20−30 30−40 40−50 50−60 60−70 70−80
Frequency 5 10 15 20 25 18 7

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Solution

C.I. Mid Value
(m)
Frequency
(f)
Deviation from Assumed mean
dx = m − A
(A = 45)
fdx f×dx2=fdx2
10 − 20
20 − 30 30 − 40
40 − 50
50 − 60
60 − 70
70 − 80
15
25
35
45=A
55
65
75
5
10
15
20
25
18
7
−30
−20
−10
0
10
20
30
−150
−200
−150
0
250
360
210
4500
4000
1500
0
2500
7200
6300
Σf = N = 100 Σfdx = 320 Σfdx2 = 26000

Calculating Mean and standard deviation through Short-cut method:Mean (X)=A+ΣfdxΣf or, X=45+320100 or, X=45+3.2 X=48.2Standard deviation (σ)=Σfdx2N-ΣfdxN2or, σ =26000100-3201002or, σ =260-3.22or, σ =260-10.24or, σ =249.76 σ =15.80

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