Q83 / 180 · KCET 2021 · Mathematics

The standard deviation of the numbers 31 , $32,33 \ldots 46,47$ is

  • A
    $\sqrt{\frac{17}{12}}$
  • B
    $\sqrt{\frac{47^{2}-1}{12}}$
  • Correct answer
    C
    $2 \sqrt{6}$
  • D
    $4 \sqrt{3}$

Solution

Given, numbers : $31,32,33, \ldots, 46,47$. The standard deviation of $31,32,33, \ldots, 47$ will be the same as those of $1,2,3, \ldots, 17$. (decreasing each item by 30 ) $\because \quad \mathrm{SD}=\sqrt{\frac{n^{2}-1}{12}}$ Here, $\quad n=17$ $\begin{aligned} \therefore \quad \mathrm{SD} &=\sqrt{\frac{17^{2}-1}{12}}=\sqrt{\frac{288}{12}} \\ &=\sqrt{24}=2 \sqrt{6} \end{aligned}$

Hence, the correct answer is option: 'C'.

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