Q253 / 270 · NDA 2023 (Phase 2) · Mathematics

If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?

  • A
    16
  • B
    6
  • C
    5
  • Correct answer
    D
    4

Solution

Since, $\sigma=\sqrt{\frac{\sum \mathrm{x}^2}{\mathrm{n}}-\left(\frac{\sum \mathrm{x}}{\mathrm{n}}\right)^2}$ $\begin{aligned} & \Rightarrow \sigma=\sqrt{\frac{16160}{10}-(40)^2} \\ & =\sqrt{1616-1600}=\sqrt{16}=4 \end{aligned}$

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

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