JEE Main & Advanced Mathematics Statistics Question Bank Measures of dispersion

  • 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                                   [DCE 1997]

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

    B)                 \[{{x}_{51}}\]

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

    D)                 \[{{x}_{50}}\]

    Correct Answer: B

    Solution :

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


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