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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Statistics

NDA 2019 · Mathematics · Statistics

Arithmetic mean of 10 observations is 60 and sum of squares of...

Arithmetic mean of 10 observations is 60 and sum of squares of deviations from 50 is 5000. What is the standard deviation of the observations?

Options

  1. A20
  2. B21
  3. C22.36
  4. D24.70

Correct answer

A. 20

Step-by-step solution

Given, xˉ=60\bar{x}=60 and n=10n=10 and ∑(xˉ−50)2=5000⇒∑(x2−100x+2500)=5000⇒∑x2−100∑x=−20000⇒∑x2=60000−20000⇒∑x2=40,000\begin{aligned} & \text{ and } \sum(\bar{x}-50)^2=5000 \\ & \Rightarrow \sum\left(x^2-100 x+2500\right)=5000 \\ & \Rightarrow \sum x^2-100 \sum x=-20000 \\ & \Rightarrow \sum x^2=60000-20000 \\ & \Rightarrow \sum x^2=40,000 \end{aligned}now,now,\begin{aligned} & \sigma=\sqrt{\frac{\sum x^2}{n}-(\bar{x})^2} \\ & \Rightarrow \sigma=\sqrt{4000-3600}=20 \end{aligned}$$
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