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 |
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 47.5.
| Class Interval | Frequency (f) | Cumulative Frequency (cf) |
| 0 - 20 | 9 | 9 |
| 20 - 40 | 16 | 9 + 16 = 25 |
| 40 - 60 | 24 | 25 + 24 = 49 |
| 60 - 80 | 15 | 49 + 15 = 64 |
| 80 - 100 | 4 | 64 + 4 = 68 |
The total frequency (N) = 68
The median position is N/2 = 68/2 = 34
The cumulative frequency of just greater than 34 is 49.
Thus, the median class = 40-60
Median = L + [(N/2 - cf)/f] × h
Where L = Lower limit of the median class = 40
N = Total frequency = 68
cf = Cumulative frequency of the class preceding the median class = 25
f = Frequency of the median class = 24
h = Class width = 20
Median = 40 + [(34 - 25)/24] × 20 = 40 + (9/24) × 20 = 40 + 7.5 = 47.5
Therefore, the median of the given data is 47.5.