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Q.

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

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a

SD < MD

b

SD > MD

c

SD = MD

d

Nothing can be said in general about the relationship between SD and MD

answer is B.

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Detailed Solution

On arranging the given observations in ascending order, we getAll negative terms 0⏟(n+1)th  term All positive termsMedian of given observations = (n + 1)th term = 0∴ SD>MD
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For (2n + 1) observations x1,−x1,x2,−x2,…,xn,−xn, and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?