JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

  • question_answer
    If \[{{x}_{1}},{{x}_{2}},\,..........\,,{{x}_{18}}\] are observations such that \[\sum\limits_{j=l}^{18}{({{x}_{j}}-8)=9}\] and \[\sum\limits_{j=l}^{18}{{{({{x}_{j}}-8)}^{2}}=45}\], then the standard deviation of these observations is

    A)  \[\sqrt{\frac{18}{34}}\]                                

    B)  5

    C)  \[\sqrt{5}\]                                       

    D)  \[\frac{3}{2}\]

    Correct Answer: D

    Solution :

    Standard deviation \[\,=\sqrt{\frac{\sum\limits_{i=1}^{18}{{{({{x}_{i}}-8)}^{2}}}}{18}\,-\left( \frac{\sum\limits_{j=1}^{18}{({{x}_{j}}-8)}}{18} \right)}\] \[=\sqrt{\frac{45}{18}\,-{{\left( \frac{9}{18} \right)}^{2}}}\,\,=\sqrt{\frac{45}{18}\ -\frac{1}{4}}\,=\sqrt{\frac{81}{36}}\,=\frac{9}{6}\,=\frac{3}{2}\]


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