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Question
For (2n+1) observation x1,−x1,x2,−x2,.....xn,−xn and 0, where xi8 are distinct, non-zero numbers. Let S.D. and M.D. denote the standard deviation and median respectively. then, which one of the following is always true?
For (2n+1) observation x1,−x1,x2,−x2,.....xn,−xn and 0, where xi8 are distinct, non-zero numbers. Let S.D. and M.D. denote the standard deviation and median respectively. then, which one of the following is always true?
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Solution
The correct option is C S.D.>M.D.
Standard deviation is an under-root function.
Hence S.D.≥0.
However in the above case, there are negative observations. Hence,Median can be negative.
Thus
S.D.>M.D.
Standard deviation is an under-root function.
Hence S.D.≥0.
However in the above case, there are negative observations. Hence,Median can be negative.
Thus
S.D.>M.D.
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