Q253 / 270 · NDA 2022 (Phase 1) · Mathematics

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

  • A
    4
  • B
    5
  • Correct answer
    C
    7
  • D
    9

Solution

Since variance $=\frac{\sum x_i^2}{n}-(x)^2$ $\begin{aligned} & 3.6=\frac{2^2+2^2+4^2+5^2+\mathrm{x}^2}{\mathrm{n}}-\left(\frac{2+2+4+5+\mathrm{x}}{\mathrm{n}}\right)^2 \\ & 3.6=\frac{4+4+16+25+\mathrm{x}^2}{5}-\left(\frac{13+\mathrm{x}}{5}\right)^2\end{aligned}$ On solving, we get $\begin{aligned} & 2 x^2-13 x-7=0 \\ & \Rightarrow \mathrm{x}=7\end{aligned}$

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

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