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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Statistics

NDA 2022 · Mathematics · Statistics

The algebraic sum of the deviations of a set of values x_1 , x_2,...

The algebraic sum of the deviations of a set of values x1x_1, x2,x3,…xnx_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?

Options

  1. A91
  2. B96
  3. C98
  4. D99

Correct answer

D. 99

Step-by-step solution

Here, (x1−100)+(x2−100)+…..+\left(\mathrm{x}_1-100\right)+\left(\mathrm{x}_2-100\right)+\ldots . .+\left(\mathrm{x}_{\mathrm{n}}-100\right)=-20hence(x1+x2+x3+…..xn)−100x=−20hence \left(x_1+x_2+x_3+\ldots . . x_n\right)-100 x=-20 Or x1+x2+x3+xn=100n−20\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\mathrm{x}_{\mathrm{n}}=100 \mathrm{n}-20 and accoding to question for same set x1+x2+x3+………..xn=92n+1408n=160⇒n=20\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\ldots \ldots \ldots . . \mathrm{x}_{\mathrm{n}}=92 \mathrm{n}+1408 \mathrm{n}=160 \Rightarrow \mathrm{n}=20 from  (i)x1+x2+x3…..+xn=1980Mean ==100×20−2020=99\begin{aligned} & \text{\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}$$
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