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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Statistics

NDA 2020 · Mathematics · Statistics

What is the standard deviation of the observations - 6 ,- 5 ,- 4...

What is the standard deviation of the observations −6,−5,−4,−1,1,4,5,6-\sqrt{6},-\sqrt{5},-\sqrt{4},-1,1, \sqrt{4}, \sqrt{5}, \sqrt{6} ?

Options

  1. A2\sqrt{2}
  2. B2
  3. C222 \sqrt{2}
  4. D4

Correct answer

B. 2

Step-by-step solution

Standard deviation =(x−xˉ)2N=\sqrt{\frac{(x-\bar{x})^2}{N}} Given data: −6,−5,−4,−1,1,4,5,6-\sqrt{6},-\sqrt{5},-\sqrt{4},-1,1, \sqrt{4}, \sqrt{5}, \sqrt{6}. \bar{x}=\frac{\text{ Sum of datas }}{\text{ Number of data }}=0(x−xˉ)2=(−6−0)2+(−5−0)2+(−4−0)2+(−1−0)2+(1−0)2+(4−0)2+(5−0)2+(6−0)2=6+5+4+1+1+4+5+6=32S.D. =(x−xˉ)2N=328=4=2\begin{aligned} & (x-\bar{x})^2=(-\sqrt{6}-0)^2+(-\sqrt{5}-0)^2+(-\sqrt{4}-0)^2+ \\ & (-1-0)^2+(1-0)^2+(\sqrt{4}-0)^2+(\sqrt{5}-0)^2+(\sqrt{6}-0)^2 \\ & =6+5+4+1+1+4+5+6=32 \\ & \text{S.D. }=\sqrt{\frac{(x-\bar{x})^2}{N}}=\sqrt{\frac{32}{8}}=\sqrt{4}=2\end{aligned}$$
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