JEE Main & Advanced Mathematics Statistics Question Bank Self Evaluation Test - Statistics

  • question_answer
    In a series of \[2n\]observations, half of them equals \['a'\] and remaining equals '__a'. If S.D. is 2, then \[\left| a \right|\] equals

    A) \[\frac{1}{n}\]

    B) \[\sqrt{2}\]

    C) \[2\]

    D) \[\frac{\sqrt{2}}{n}\]  

    Correct Answer: C

    Solution :

    [c] \[\because \sigma =\sqrt{\frac{\Sigma x{{i}^{2}}}{N}-{{\left( \frac{\Sigma {{x}_{i}}}{N} \right)}^{2}}}\] \[\therefore 2=\sqrt{\frac{({{a}^{2}}+{{a}^{2}}...'2n'times)}{2n}-0}\] \[\Rightarrow 4=\frac{2n{{a}^{2}}}{2n}\Rightarrow {{a}^{2}}=4\Rightarrow \left| a \right|=2\]


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