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JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    Consider any set of observations \[{{x}_{1}},\,{{x}_{2}},\,....,\,\,{{x}_{10}},\] 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 is equal to

    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 \[{{r}_{1}}:{{r}_{2}}:{{r}_{3}}=1:4:9\]th i.e,, 51th term \[{{V}_{1}}={{V}_{2}}\]


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