Following data shows the marks obtained by 100 students in a class test : The median will be the average of which two observations ?
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
Option C: 28 and 29
Since n = 100 (even), median = average of 50th and 51st observations. From cumulative frequency table, cumulative frequency up to marks 28 is 50, and up to 29 is 78. So the 50th observation is 28 and 51st is 29.
Source: Chapter 13, Section 13.4 Median of Grouped Data
Explanation
- Arrange data in ascending order and build a cumulative frequency table.
- For even n, median = average of (n/2)th and (n/2 + 1)th = 50th and 51st observations.
- CF up to 28 = 6+20+24 = 50, so the 50th observation is 28; CF up to 29 = 78, so the 51st observation is 29.
- Examiners expect you to identify the correct pair using the cumulative frequency table — not just guess from the options.