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JEE Main & Advanced Mathematics Statistics Question Bank Mock Test - Statistics

  • question_answer
    For\[\left( 2n+1 \right)\] observations \[{{x}_{1}},{}^{-}{{x}_{1}},\,\,{{x}_{2}},{}^{-}{{x}_{2}},\,\,...,\,\,{{x}_{n}},\,{{\,}^{-}}{{x}_{n}}\] and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?

    A) SD>MD

    B) SD>MD

    C) SD=MD

    D) Nothing can be said in general about the relationship between SD and MD

    Correct Answer: B

    Solution :

    [b] on arranging the given observations in ascending order, we get All negative terms \[\underbrace{\,\,\,\,\,\,\,\,O\,\,\,\,\,\,\,\,}_{{{(n+1)}^{th}}\,\,\text{term}}\]all positive terms Median of given observations\[=(n+1)\]th term=0 \[\therefore \,\,\,SD>MD\]


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