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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

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

    A)  9                                

    B)  12              

    C)  15                              

    D)  18

    Correct Answer: D

    Solution :

     Since, Root mean square \[\ge \] Arithmetic mean \[\therefore \]    \[\sqrt{\frac{\Sigma x_{i}^{2}}{n}}\ge \,\frac{\Sigma {{x}_{i}}}{n}\] \[\Rightarrow \]            \[\sqrt{\frac{400}{n}}\ge \frac{80}{n}\] \[\Rightarrow \]            \[\frac{20}{\sqrt{n}}\ge \frac{80}{n}\] \[\Rightarrow \]            \[\sqrt{n}\ge 4\] \[\Rightarrow \]            \[n\ge 16\]


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