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JEE Main & Advanced Mathematics Statistics Question Bank Measures of dispersion

  • question_answer
    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 [Orissa JEE 2002]

    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.

    Correct Answer: B

    Solution :

                       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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