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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Statistics

NDA 2023 · Mathematics · Statistics

The sum of deviations of n numbers from 10 and 20 are p and q...

The sum of deviations of n numbers from 10 and 20 are pp and qq respectively. If (p−q)2=10000(p-q)^2=10000, then what is the value of nn ?

Options

  1. A10
  2. B20
  3. C50
  4. D100

Correct answer

A. 10

Step-by-step solution

 Since, ∑(xi−10)=P and  ∑(xi−20)=q⇒∑xi−10n=P∑xi−20n=q\begin{aligned} & \text{ Since, } \sum\left(\mathrm{x}_{\mathrm{i}}-10\right)=\mathrm{P} \\ & \text{\text{ and } } \sum\left(\mathrm{x}_{\mathrm{i}}-20\right)=\mathrm{q} \\ & \Rightarrow \sum \mathrm{x}_{\mathrm{i}}-10 \mathrm{n}=\mathrm{P} \\ & \sum \mathrm{x}_{\mathrm{i}}-20 \mathrm{n}=\mathrm{q} \end{aligned} Now, (−10n+20n)2=10000⇒100n2=10000⇒n=10(-10 \mathrm{n}+20 \mathrm{n})^2=10000\Rightarrow 100 \mathrm{n}^2=10000 \Rightarrow \mathrm{n}=10
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