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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Statistics

NDA 2023 · Mathematics · Statistics

If the mean and the sum of squares of 10 observations are 40 and...

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

Options

  1. A16
  2. B6
  3. C5
  4. D4

Correct answer

D. 4

Step-by-step solution

Since, \sigma=\sqrt{\frac{\sum \mathrm{x}^2}{\mathrm{n}}-\left(\frac{\sum \mathrm{x}}{\mathrm{n}}\right)^2}⇒σ=1616010−(40)2=1616−1600=16=4\begin{aligned} & \Rightarrow \sigma=\sqrt{\frac{16160}{10}-(40)^2} \\ & =\sqrt{1616-1600}=\sqrt{16}=4 \end{aligned}
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