Q256 / 270 · NDA 2022 (Phase 1) · Mathematics

The algebraic sum of the deviations of a set of values $x_1$, $x_2, x_3, \ldots x_n$ measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92 is 140 . What is the mean of the values?

  • A
    91
  • B
    96
  • C
    98
  • Correct answer
    D
    99

Solution

Here, $\left(\mathrm{x}_1-100\right)+\left(\mathrm{x}_2-100\right)+\ldots . .+\left(\mathrm{x}_{\mathrm{n}}-100\right)=-20$ hence $\left(x_1+x_2+x_3+\ldots . . x_n\right)-100 x=-20$ Or $\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+$ $\mathrm{x}_{\mathrm{n}}=100 \mathrm{n}-20$ and accoding to question for same set $\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\ldots \ldots \ldots . . \mathrm{x}_{\mathrm{n}}=92 \mathrm{n}+140$ $8 \mathrm{n}=160 \Rightarrow \mathrm{n}=20$ $\begin{aligned} & \text { from }(\mathrm{i}) \mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3 \ldots . .+\mathrm{x}_{\mathrm{n}}=1980 \\ & \text {Mean }==\frac{100 \times 20-20}{20}=99\end{aligned}$

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

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