Q270 / 270 · NDA 2024 (Phase 1) · Mathematics
The marks obtained by 10 students in a Statistics test are $24,47,18,32,19,15,21,35,50$ and 41.
What is the variance of the largest five observations?
- A14.6
- B21.8
- C25.2
- Correct answerD46.8
Solution
$\because 15,18,19,21,24,32,35,41,47,50$
Largest 5 observations are $32,35,41,47,50$
$\begin{aligned}
\text { Mean } & =\mu=\frac{32+35+41+47+50}{5} \\
& =\frac{205}{5}=41
\end{aligned}$
$\begin{aligned} \sigma^2 & =\frac{\Sigma\left(x_i-\mu\right)^2}{5} \\ & =\frac{9^2+6^2+0^2+6^2+9^2}{5} \\ & =\frac{234}{5}=46.8\end{aligned}$
Hence, the correct answer is option: 'D'.