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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Statistics

NDA 2023 · Mathematics · Statistics

The mean and variance of five observations are 14 and 13.2...

The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11,16 and 20. What are the other two observations?

Options

  1. A8 and 15
  2. B9 and 14
  3. C10 and 13
  4. D11 and 12

Correct answer

C. 10 and 13

Step-by-step solution

xˉ=14,Var⁡(x)=13.2\bar{x}=14, \operatorname{Var}(x)=13.2 Observations =11,16,20,a,bxˉ=11+16+20+a+b5=14a+b=23=11,16,20, a, b\bar{x}=\frac{11+16+20+a+b}{5}=14a+b=23....(1) var⁡(X)=Σxi2n−(xˉ)213.2=112+162+202+a2+b25−(14)266=777−980+a2+b2a2+b2=269\operatorname{var}(X)=\frac{\Sigma x_i^2}{n}-(\bar{x})^213.2=\frac{11^2+16^2+20^2+a^2+b^2}{5}-(14)^266=777-980+a^2+b^2a^2+b^2=269.....(2) By (1) \& (2). we get ∴a=13,b=10\therefore \quad a=13, b=10
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