The median is the middle value when data is arranged in order.
Total frequency n=55
Median position =2n+1
=255+1
=256
=28
The median is the 28th value in the data.
Constructing the cumulative frequency table:
| Variable | Frequency | Cumulative Frequency |
|---|---|---|
| 11 | 5 | 5 |
| 12 | 7 | 12 |
| 13 | 11 | 23 |
| 14 | 9 | 32 |
| 15 | 8 | 40 |
| 16 | 7 | 47 |
| 17 | 3 | 50 |
| 18 | 5 | 55 |
The 28th value needs to be located:
After variable 13: cumulative frequency = 23 (less than 28)
After variable 14: cumulative frequency = 32 (greater than 28)
The 28th value falls in the class with variable 14.
Therefore, the median is 14.