Consider the following frequency distribution.
|
Class |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |
|
Frequency |
4 |
5 |
7 |
10 |
12 |
8 |
4 |
Find the median of the distribution?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 39
Given Frequency Distribution:
| Class | Frequency (f) | Cumulative Frequency (CF) |
|---|---|---|
| 0 - 10 | 4 | 4 |
| 10 - 20 | 5 | 9 |
| 20 - 30 | 7 | 16 |
| 30 - 40 | 10 | 26 |
| 40 - 50 | 12 | 38 |
| 50 - 60 | 8 | 46 |
| 60 - 70 | 4 | 50 |
Total frequency (N) = 50
Median Class: The class whose cumulative frequency is just greater than or equal to 25 (N/2)
→ Median class = 30 – 40
Values:
- $l = 30$
- $f = 10$ (frequency of median class)
- $F = 16$ (cumulative frequency before median class)
- $h = 10$ (class width)
Median formula:
$\text{Median} = l + \frac{\frac{N}{2} - F}{f} \cdot h$
Substituting:
$\text{Median} = 30 + \frac{25 - 16}{10} \cdot 10 = 30 + \frac{9}{10} \cdot 10 = 30 + 9 = 39$