A survey of 45 students produced the following frequency distribution for their scores (out of 60): 0‑10: 4, 10‑20: 7, 20‑30: 10, 30‑40: 12, 40‑50: 9, 50‑60: 3. Find the median score of the class. (Choose the correct option.)

Step-by-step solution

1. Compute cumulative frequencies: up to 10 →4, up to 20 →11, up to 30 →21, up to 40 →33, up to 50 →42, up to 60 →45.
2. Find the median position: $\frac{n+1}{2}=\frac{45+1}{2}=23$th student.
3. Locate the class containing the median: 23rd lies between 21 and 33, so in class 30‑40.
4. Let $L=30$, $h=10$, $F=21$ (cumulative before the median class), and $f=12$ (frequency of the median class).
5. Apply the interpolation formula: $M=L+\frac{(n+1)/2-F}{f}\times h$. $M=30+\frac{23-21}{12}\times 10=30+\frac{2}{12}\times 10=30+1.6667\approx 31.67$.
6. Thus the median score is approximately $31.67$.

Concept tested: Median for grouped data

Published 7 October 2026 · How this solution was prepared and checked