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Question

Calculate the standard deviation for the following data:
Class: 0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequency: 9 17 43 82 81 44 24

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Solution

Class fi Midpointxi yi=xi-10530 yi2 fiyi fiyi2
030 9 15 3 9 27 81
3060 17 45 2 4 34 68
6090 43 75 1 1 43 43
90120 82 105 0 0 0 0
120150 81 135 1 1 81 81
150180 44 165 2 4 88 176
180210 24 195 3 9 72 216
fi=N=300 fiyi=137 fiyi2=665
Mean, x¯=a+h1NΣfiyi=105+30137300=118.7

Variance:
σ2=h2N2Nfiyi2-fiyi2=90090000300×665-18769=1100199500-18769=180731100=1807.31SD, σ = 1807.31 = 42.51

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