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Q.

For (2n+1) observations x1,−x1,x2,−x2,…,xn,−xn and 0 ,  whereall x 's are distinct, let SD and MD denote the  standard deviationand median respectively. Then which  of the following is always true?

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a

SD < MD

b

SD > MD

c

SD = MD

d

None of these

answer is B.

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Detailed Solution

on arranging the given observations in ascending order, we get  All negative terms O⏟(n+1)th  term  All positive terms Median of given observations = (n + 1) th term = 0 ∴SD>MD
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