Find the median of the following data:

- Class Interval: 0 - 20, 20 - 40, 40 - 60, 60 - 80, 80 - 100
- Frequency: 9, 16, 24, 15, 4

Question

Find the median of the following data:

- Class Interval: 0 - 20, 20 - 40, 40 - 60, 60 - 80, 80 - 100
- Frequency: 9, 16, 24, 15, 4

Accepted Answer

**Solution:**

1. Calculate the total frequency, $ N = 9 + 16 + 24 + 15 + 4 = 68 $.

2. Find $ \frac{N}{2} = 34 $.

3. Determine the cumulative frequency for each class interval:

| Class Interval | Frequency | Cumulative Frequency |
|----------------|-----------|----------------------|
| 0-20           | 9         | 9                    |
| 20-40          | 16        | 25                   |
| 40-60          | 24        | 49                   |
| 60-80          | 15        | 64                   |
| 80-100         | 4         | 68                   |

4. Identify the median class as the class where cumulative frequency just exceeds $ \frac{N}{2} $. Here, it is the class 40-60 because cumulative frequency before it is 25 and after it is 49.

5. Use the median formula:

$$
\text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \times h
$$

Where:
- $ L = 40 $ (lower boundary of median class)
- $ CF = 25 $ (cumulative frequency before median class)
- $ f = 24 $ (frequency of median class)
- $ h = 20 $ (class width)

6. Substitute values:

$$
\text{Median} = 40 + \left( \frac{34 - 25}{24} \right) \times 20 = 40 + \frac{9}{24} \times 20 = 40 + 7.5 = 47.5
$$

**Answer:** $47.5$

Answer

Answer

Answer