Question

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

Answer 1

Answer: (B)

On arranging the given observations in ascending order, we get
All negative terms All positive terms
The median of given observations $=(n+1{)}^{th}term=0$
$\therefore S.D.>M.D.$