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Question

Find the mean and variance for the following frequency distribution
Classes0-3030-6060-9090-120120-150150-180180-210
Frequencies23510352

Solution
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Class fi xi ui=xiAh u2ifiui fiu2i
0-30 2 15 -3 9 -6 18
30-60 3 45 -2 4 -6 12
60-90 5 75 -1 1 -5 5
90-120 10 105 0 0 0 0
120-150 3 135 1 1 3 3
150-180 5 165 2 4 10 20
180-210 2 195 3 9 6 18
Total 30 2 76
Here, N=30,h=30
Mean, ¯x=A+7i=1fiuiN×h
=105+230×30
=105+2=107

Variance (σ2)=h2N2N7i=lfiu2i(7i=lfiui)2
=(30)2(30)2[30×76(2)2]
=22804
=2276

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