1. Tardigrade
  2. Question
  3. Mathematics
  4. For (2n + 1) observations x1, -x1, x2, -x2, .........xn, -xn 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?

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Q. 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?

Statistics

Solution:

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