Final answer:
The median length of the leaves is calculated by ordering the data and finding the middle value. With 40 leaves, the median is the average of the 20th and 21st values, which both fall within the 145–153 mm range, resulting in a median length of 149 mm.
Step-by-step explanation:
To find the median length of the leaves, we'll need to order the data and find the middle value. Since there are 40 leaves in total, the median will be the average of the 20th and 21st values. First, we'll determine how many leaves fall into each length category:
- 118–126 mm: 3 leaves
- 127–135 mm: 5 leaves
- 136–144 mm: 9 leaves
- 145–153 mm: 12 leaves
- 154–162 mm: 5 leaves
- 163–171 mm: 4 leaves
- 172–180 mm: 2 leaves
The cumulative count of leaves up to the 153 mm category is 29 (3 + 5 + 9 + 12), which exceeds the halfway point of 20. Thus, both the 20th and 21st leaves fall within the 145–153 mm length category. To find the median, since all leaves in this category are assumed to be of equal length within the range, we can take the average of the endpoints: (145 + 153) / 2 = 149 mm. Hence, the median length of the leaves is 149 mm.