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Question

Find the mean and variance for the following frequency distrubution
Classes0-1010-2020-3030-4040-50
Frequencies5815166

Solution
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Class intervalfixi ui=xiAh u2i fiui fiu2i
0-10 5 5 -2 4 -10 20
10-20 8 15 -1 1 -8 8
20-30 1525 0 0 0 0
30-40 1635 1 1 16 16
40-50 6 452 4 12 24
Total 50 10 68
We have N=fi=50
Width of class h=10
Assumed mean A=25(say)

Mean, ¯x=A+5i=1fiuiN×h
=25+1050×10=25+2=27
¯x=27

Variance σ2=h25i=1fiu2iN(5i=1fiuiN)2
σ2=102[6850(1050)2]
=102[50×68(10)2](50)2
=125[3400100]
=330025
=132

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