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$For (2 n + 1) observations x_{1}, - x_{1}, x_{2}, - x_{2}, \dots, x_{n}, - x_{n} and 0,$
$where all x's are distinct, let SD and MD denote the standard deviation$
$and median respectively. Then which of the following is always true?$

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SD < MD

SD > MD

SD = MD

None of these

answer is B.

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Detailed Solution

on arranging the given observations in ascending order, we get

$All negative terms \underset{(n + 1)^{th} term}{\underset{⏟}{O}} All positive terms$

Median of given observations = (n + 1) ^th term = 0

$∴ SD > MD$

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