JEE Main & Advanced Mathematics Statistics Question Bank Self Evaluation Test - Statistics

  • question_answer
    Consider any set of observations \[{{x}_{1}},{{x}_{2}},{{x}_{3,...}}{{x}_{101}};\] it being given that \[{{x}_{1}}<{{x}_{2}}<{{x}_{3}}<...<{{x}_{100}}<{{x}_{101}};\] then the mean deviation of this set of observations about a point k is minimum when k equals

    A) \[{{x}_{1}}\]

    B) \[{{x}_{51}}\]

    C) \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\]

    D) \[{{x}_{50}}\]

    Correct Answer: B

    Solution :

    [b] Mean deviation is minimum when it is considered about the item, equidistant from the beginning and end i.e. the median. In case median is \[\frac{101+1}{2}\]th i.e., 51st item i.e., \[{{x}_{51}}.\]


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