2024 · Q54
Consider the following for the next two items that follow: A frequency distribution is as follows: Marks: 18–26, 27–35, 36–44, 45–53, 54–62, 63–71, 72–80; Number of Students: 5, 7, 10, 15, 8, 3, 2. What is the median of the distribution?
Elementary MathematicsStatistics
- A44.9
- B45.5
- C45.9
- D46.3
Explanation
With continuity correction the classes become 17.5–26.5 (5), 26.5–35.5 (7), 35.5–44.5 (10), 44.5–53.5 (15), and so on. Cumulative frequencies are 5, 12, 22, 37, so the middle (25th of N = 50) item falls in 44.5–53.5. Median = L + ((N/2 − cf)/f)×h = 44.5 + ((25−22)/15)×9 = 46.3. This is option D.