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Question

There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test

MarksFrequency0x21x2x23(x+1)242x5x+1

Where x is positive integer. Then the variance of the marks is

A
1.26
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B
1.28
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C
1.34
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D
1.24
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Solution

The correct option is A 1.26
Sum of frequencies
fi=60
x2+x+x2+(x+1)2+2x+x+1=602x2+7x60=0(x4)(2x+15)=0x=4(As x2 is frequency, so x20)

Now,
xififixifix2i0200144421632643257522548321285525125fixi=168fix2i=546

¯¯¯x=fixifi=16860=2.8

σ2=1Nfix2i(¯¯¯x)2
=54660(2.8)2=1.26

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