Q269 / 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 mean deviation of the largest five observations?

  • A
    4.8
  • B
    5.5
  • Correct answer
    C
    6
  • D
    7.5

Solution

$\because 15,18,19,21,24,32,35,41,47,50$ Largest 5 observations are $32,35,41,47,50$ $\begin{aligned} \text { Mean } & =\mu=\frac{32+35+41+47+50}{5} \\ & =\frac{205}{5}=41 \end{aligned}$ Mean deviation $=\frac{\Sigma\left|x_i-\mu\right|}{n}$ $\begin{aligned} & =\frac{|32-41|+|35-41|+|41-41|+|47-41|+|50-41|}{5} \\ & =\frac{9+6+0+6+9}{5}=\frac{30}{5}=6\end{aligned}$

Hence, the correct answer is option: 'C'.

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