Meaning: This question gives data in class intervals with their frequencies. We calculate the mean by using the midpoint of each class interval.
Formula:
Where:
- \(f\) = Frequency
- \(m\) = Midpoint
- \(fm\) = Frequency × Midpoint
Step 1: Prepare the table.
| Class interval | Midpoint (m) | f | fm |
|---|---|---|---|
| 20–40 | 30 | 2 | 60 |
| 40–60 | 50 | 7 | 350 |
| 60–80 | 70 | 9 | 630 |
| 80–100 | 90 | 24 | 2160 |
| 100–120 | 110 | 9 | 990 |
| 120–140 | 130 | 7 | 910 |
| 140–160 | 150 | 2 | 300 |
| Total | 60 | 5400 |
Step 2: Find the total frequency.
Step 3: Find the total of fm.
Step 4: Calculate the mean.
Final Answer: 90.0
Remember for exams:
- Find the midpoint of every class interval.
- Multiply midpoint by frequency.
- Calculate total frequency and total \(fm\).
- Divide total \(fm\) by total frequency.
