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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    If \[\mathbf{n}=\mathbf{10},\overline{\mathbf{x}}=\mathbf{12},\sum {{\mathbf{x}}^{\mathbf{2}}}=\mathbf{1530}\], then the coefficient of variance is:

    A)  \[20%\]                        

    B)  \[25%\]         

    C)  \[30%\]                        

    D)  \[35%\]

    Correct Answer: B

    Solution :

    [b] \[\because S.D.(\sigma )=\sqrt{\frac{\sum {{x}^{2}}}{n}-{{\left( \frac{\sum x}{n} \right)}^{2}}}=\sqrt{\frac{1530}{10}-{{(12)}^{2}}}\]Variance \[={{\left( S.D \right)}^{2}}={{\sigma }^{2}}=9.\]  Coefficient of variance \[=\frac{\sigma }{\overline{x}}\times 100=\frac{3\times 100}{12}=25%\] Hence option [b] is correct.


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