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JEE Main & Advanced Mathematics Statistics Question Bank Critical Thinking

  • question_answer
    In a series of 2n observations, half of them equal to a and remaining half equal to ?a. If the standard deviation of the observations is 2, then |a| equals                     [AIEEE 2004]

    A)                 \[\frac{\sqrt{2}}{n}\]           

    B)                 \[\sqrt{2}\]

    C)                 2             

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

    Correct Answer: C

    Solution :

                    Let a, a, ........n times and ? a, ? a, ? a, ? a, ........n times i.e., mean = 0  and  S.D.\[=\sqrt{\frac{n{{(a-0)}^{2}}+n{{(-a-0)}^{2}}}{2n}}\]                         \[2=\sqrt{\frac{n{{a}^{2}}+n{{a}^{2}}}{2n}}=\sqrt{{{a}^{2}}}=\pm a\]. Hence \[|a|\ =2\].


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