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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Statistics

NDA 2019 · Mathematics · Statistics

If all the natural numbers between 1 and 20 are multiplied by 3 ,...

If all the natural numbers between 1 and 20 are multiplied by 3 , then what is the variance of the resulting series ?

Options

  1. A99.75
  2. B199.75
  3. C299.25
  4. D399.25

Correct answer

C. 299.25

Step-by-step solution

The series is 1,2,3,……201,2,3, \ldots \ldots 20 Variance (σ)=Σx2n−Σ(xˉ)2(\sigma)=\frac{\Sigma x^2}{n}-\Sigma(\bar{x})^2=n(n+1)(2n+1)6n−(n(n+1)2n)2=(n+1)12(n−1)=n2−112=(20)2−112=39912=1334=33.25\begin{aligned} & =\frac{n(n+1)(2 n+1)}{6 n}-\left(\frac{n(n+1)}{2 n}\right)^2 \\ & =\frac{(\mathrm{n}+1)}{12}(\mathrm{n}-1) \\ & =\frac{n^2-1}{12}=\frac{(20)^2-1}{12}=\frac{399}{12}=\frac{133}{4}=33.25\end{aligned}∵\because Numbers are multiplied by 3 , variance (σ)=33.25×9=299.25(\sigma)=33.25 \times 9=299.25
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