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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Statistics

NDA 2022 · Mathematics · Statistics

The variance of five positive observations is 3.6. If four of the...

The variance of five positive observations is 3.6. If four of the observations are 2,2,4,52,2,4,5 then what is the remaining observation?

Options

  1. A4
  2. B5
  3. C7
  4. D9

Correct answer

C. 7

Step-by-step solution

Since variance =∑xi2n−(x)2=\frac{\sum x_i^2}{n}-(x)^23.6=22+22+42+52+x2n−(2+2+4+5+xn)23.6=4+4+16+25+x25−(13+x5)2\begin{aligned} & 3.6=\frac{2^2+2^2+4^2+5^2+\mathrm{x}^2}{\mathrm{n}}-\left(\frac{2+2+4+5+\mathrm{x}}{\mathrm{n}}\right)^2 \\ & 3.6=\frac{4+4+16+25+\mathrm{x}^2}{5}-\left(\frac{13+\mathrm{x}}{5}\right)^2\end{aligned}Onsolving,wegetOn solving, we get\begin{aligned} & 2 x^2-13 x-7=0 \\ & \Rightarrow \mathrm{x}=7\end{aligned}$$
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