For (2n+1) observations x_1 , , - x_1 , x_2 , , - x_2 , ,..... x_… - Vidyadip

MCQ

For $(2n+1)$ observations ${x_1},\, - {x_1}$, ${x_2},\, - {x_2},\,.....{x_n},\, - {x_n}$ and $0$ where $x$’s are all distinct. Let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Then which of the following is always true

A
$S.D. < M.D.$
✓
$S.D. > M.D.$
C
$S.D. = M.D.$
D
Nothing can be said in general about the relationship of $S.D.$ and $M.D.$

✓

Answer

Correct option: B.

$S.D. > M.D.$

b
(b) On arranging the given observations in ascending order, we get

All negative terms $\underbrace {\,\,O\,\,}_{{{(n + 1)}^{th}}\ term}$ All positive terms

The median of given observations $ = {(n + 1)^{th}}$ term = $0$

$ S. D. > M .D.$

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