To find the five-number summary of the data from Tray 1 (with fertilizer), we need to examine its dataset and determine the following key values:
1. Minimum: The smallest number in the dataset.
2. First Quartile (Q1): The median of the lower half of the dataset.
3. Median (Q2): The middle number when the dataset is sorted.
4. Third Quartile (Q3): The median of the upper half of the dataset.
5. Maximum: The largest number in the dataset.
Given the heights from Tray 1 are:
[tex]\[22, 48, 29, 30, 35, 54, 37, 56.5947404472, 66\][/tex]
First, let's sort these values in ascending order:
[tex]\[22, 29, 30, 35, 37, 48, 54, 56.5947404472, 66\][/tex]
Now we can identify the five-number summary:
1. Minimum:
The smallest value in the sorted list is 22.
2. First Quartile (Q1):
Q1 is the median of the first half of the dataset. The lower half is [tex]\[22, 29, 30, 35\][/tex].
The median of this subset is: [tex]\( \frac{29 + 30}{2} = 29.5 \)[/tex].
However, in calculations using correct percentiles, we found Q1 to be 30.
3. Median (Q2):
The median of the entire sorted dataset is 37.
4. Third Quartile (Q3):
Q3 is the median of the upper half of the dataset. The upper half is [tex]\[48, 54, 56.5947404472, 66\][/tex].
The median of this subset is: [tex]\( \frac{54 + 56.5947404472}{2} = 55.2973702236 \)[/tex].
However, in calculations using correct percentiles, we found Q3 to be 54.
5. Maximum:
The largest value in the sorted list is 66.
Thus, the five-number summary for the data from Tray 1 is:
[tex]\[22, 30, 37, 54, 66\][/tex]
So the correct answer among the provided options is not listed, but [22, 35, 37, 54, 66] would've been the closest to match had that option been there. It's important to check the exact box plot requirements, as exact calculations can differ especially with floating point intricacies, but the concept applies correctly.
