The median of the frequency distribution:
| Marks | Number of students |
|---|---|
| 0-5 | 7 |
| 5-10 | 5 |
| 10-15 | 2 |
| 15-20 | 4 |
| 20-25 | 1 |
| 25-30 | 6 |
| 30-35 | 3 |
| 35-40 | 8 |
| 40-45 | 9 |
| 45-50 | 5 |
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30
The median is the middle value when all the marks are in order. For grouped data it lies in the median class, the first class whose cumulative frequency reaches \(\frac{N}{2}\), and is found by \(\displaystyle l+\frac{\frac{N}{2}-cf}{f}\times h\), where \(l\) is the lower limit of that class, \(cf\) the cumulative frequency before it, \(f\) its frequency and \(h\) the class width.
Cumulative frequencies:
0-5: 7; 5-10: 12; 10-15: 14; 15-20: 18; 20-25: 19
25-30: 25; 30-35: 28; 35-40: 36; 40-45: 45; 45-50: 50
The median (N = 50, so half of N is 25):
The cumulative frequency first reaches 25 in the class 25-30: \(l=25\), \(cf=19\), \(f=6\), \(h=5\)
Median \(\displaystyle =25+\frac{25-19}{6}\times5=25+5=30\)
The 25th student is the last one of the class 25-30, so the median falls at its upper limit, 30.