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Question

In a data set consisting of 10 values
x1,x2,....,x10 such that 10xi10 with mean 0, what can be the maximum standard deviation?

A
10
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B
100
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C
81
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D
Insufficient data
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Solution

The correct option is A 10
Variance = (xi¯x)2NSince ¯x=0Variance = (xi)2N = (xi)210

The maximum xi2 can be 102. Let us see if each xi2 can be made 102 then we would really get the maximum value of variance that is 100 and SD will be 10. If we choose the data set to be{-10,-10,-10,-10,-10,10,10,10,10,10} then the mean will be 0.
Hence maximum SD is 10.

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