Mathematics
Mathematics
Problem
The frequency distribution for the marks of 50 students is given below:| Marks (Class interval) | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 |
|---|---|---|---|---|---|
| Number of students | 5 | 9 | ? | 12 | 4 |
Intuitive explanation
The median is the middle value of a dataset, and for grouped data it falls in the class interval where cumulative frequency first reaches or exceeds half the total. Since you know the median is 25.5 (which lies in the 20–30 interval), you can set up an equation using the median formula for grouped data: the cumulative frequency up to the median class must equal exactly half of 50. Work backwards from this constraint to find the missing frequency.
Intuitive explanation
The median is the middle value of a dataset, and for grouped data it falls in the class interval where cumulative frequency first reaches or exceeds half the total. Since you know the median is 25.5 (which lies in the 20–30 interval), you can set up an equation using the median formula for grouped data: the cumulative frequency up to the median class must equal exactly half of 50. Work backwards from this constraint to find the missing frequency.