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Question

Let r be the range and S2=1n1ni=1(xi¯¯¯x)2, where S is the S.D. of a set of observations x1,x2.....xn, then

A
Srnn1
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B
S=rnn1
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C
Srnn1
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D
None of these
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Solution

The correct option is A Srnn1
We have r=max|xiyj|
And S2=1n1ni=1(xi¯¯¯x)2
Now,(xi¯¯¯x)2=(xix1+x2+....+xnn)2
=1n2[(xix1)+(xix2)+....+(xixi1)+(xixi+1)+...+(xixn)]1n2[(n1)r]2,(xi¯¯¯x)2r2ni=1(xi¯¯¯x)2nr2

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