UPSC NDA I 2024 Mathematics Paper

Concept:Mean deviation measures the average absolute deviation of data points from the mean.Explanation:The marks of 10 students (given in the question) are sorted in ascending order: $15, 18, 19, 21, 24, 32, 35, 41, 47, 50$.The largest five observations are: $32, 35, 41, 47, 50$.Calculate the mean of these five numbers: $\text{Mean} = \frac{32+35+41+47+50}{5} = \frac{205}{5} = 41$.Now compute each absolute deviation from the mean: $|32-41|=9$, $|35-41|=6$, $|41-41|=0$, $|47-41|=6$, $|50-41|=9$.Sum of these deviations: $9+6+0+6+9 = 30$.Mean deviation = $\frac{30}{5} = 6$.Answer:$6$ (Option C).