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JCECE Engineering JCECE Engineering Solved Paper-2013

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

    A) \[9\]                                     

    B) \[12\]

    C) \[15\]                                   

    D) \[18\]

    Correct Answer: C

    Solution :

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


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