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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Statistics

NDA 2024 · Mathematics · Statistics

The marks obtained by 10 students in a Statistics test are...

The marks obtained by 10 students in a Statistics test are 24,47,18,32,19,15,21,35,5024,47,18,32,19,15,21,35,50 and 41. What is the variance of the largest five observations?

Options

  1. A14.6
  2. B21.8
  3. C25.2
  4. D46.8

Correct answer

D. 46.8

Step-by-step solution

∵15,18,19,21,24,32,35,41,47,50\because 15,18,19,21,24,32,35,41,47,50 Largest 5 observations are 32,35,41,47,5032,35,41,47,50 Mean =μ=32+35+41+47+505=2055=41\begin{aligned} \text{ Mean } & =\mu=\frac{32+35+41+47+50}{5} \\ & =\frac{205}{5}=41 \end{aligned}$\begin{aligned} \sigma^2 & =\frac{\Sigma\left(x_i-\mu\right)^2}{5} \\ & =\frac{9^2+6^2+0^2+6^2+9^2}{5} \\ & =\frac{234}{5}=46.8\end{aligned}
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