JEE Main & Advanced Mathematics Statistics Question Bank Mean

  • question_answer
    Let \[{{x}_{1}},\,{{x}_{2}},....,{{x}_{n}}\] be n observations such that \[\sum x_{i}^{2}=400\] and \[\sum x_{i}^{{}}=80\]. Then a possible value of n among the following is          [AIEEE 2005]

    A)                 9             

    B)                 12

    C)                 15           

    D)                 18

    Correct Answer: D

    Solution :

               Since, root mean square ³ arithmetic mean                    \ \[\sqrt{\frac{\sum\limits_{i=1}^{n}{x_{i}^{2}}}{n}}\ge \frac{\sum\limits_{i=1}^{n}{{{x}_{i}}}}{n}=\sqrt{\frac{400}{n}}\ge \frac{80}{n}\Rightarrow n\ge 16\]                 Hence, possible value of n = 18.


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