Question
Question: For (2n+1) observations \(x_{1}, - x_{1}\), \(x_{2}, - x_{2},.....x_{n}, - x_{n}\) and 0 where x’s a...
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
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
S.D. > M.D.
Explanation
Solution
On arranging the given observations in ascending order, we get All negative terms (n+1)thterm︸O All positive terms
The median of given observations =(n+1)thterm = 0
∴ S. D. > M .D.