Find the **median** of the following data:

| Class Interval | Frequency |
|---------------|-----------|
| 0 – 20 | 9 |
| 20 – 40 | 16 |
| 40 – 60 | 24 |
| 60 – 80 | 15 |
| 80 – 100 | 4 |

Question

Find the **median** of the following data:

| Class Interval | Frequency |
|---------------|-----------|
| 0 – 20        | 9         |
| 20 – 40       | 16        |
| 40 – 60       | 24        |
| 60 – 80       | 15        |
| 80 – 100      | 4         |

Accepted Answer

**Solution:**

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

2. Determine the median position:
   - ( $\frac{N}{2}$ = $\frac{68}{2}$ = 34 )

3. Find the cumulative frequencies to locate the median class:
   - 0 – 20: 9
   - 20 – 40: 9 + 16 = 25
   - 40 – 60: 25 + 24 = 49

Since 34 lies between 25 and 49, the median class is **40 – 60**.

4. Identify parameters for the median formula:
   - Lower boundary, $ L = 40 $
   - Cumulative frequency before median class, $ CF = 25 $
   - Frequency of median class, $ f = 24 $
   - Class width, $ h = 20 $

5. Apply the median formula:
   $$
   \text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \times h
   = 40 + \left( \frac{34 - 25}{24} \right) \times 20
   = 40 + \frac{9}{24} \times 20
   = 40 + 7.5 = 47.5
   $$

**Answer:** $47.5$

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