The following frequency distribution shows the number of students scoring in different ranges on a test: | Score range | Frequency | |-------------|-----------| | 0-20 | 5 | | 20-40 | 8 | | 40-60 | 12 | | 60-80 | 7 | | 80-100 | 3 | Find the class mark of the modal class and approximate mean score using the mid‑point method.

Step-by-step solution

1. Identify modal class: 40–60 has highest frequency 12.
2. Compute its class mark (midpoint): $(40+60)/2=50$.
3. Compute midpoints of all classes: 10, 30, 50, 70, 90.
4. Compute weighted sum: $10\ast 5+30\ast 8+50\ast 12+70\ast 7+90\ast 3=1650$.
5. Total frequency: $5+8+12+7+3=35$.
6. Approximate mean: $1650div35approx47.1$.

Concept tested: Frequency distribution and mid‑point method

Published 13 October 2026 · How this solution was prepared and checked