The stem-and-leaf plot represents the average monthly high temperatures in Tampa, Florida. What is the third quartile (Q3) of the temperatures?
stem 6 leaf 9, stem 7 leaves 1 2 6 7, stem 8 leaves 1 4 7 9 9, stem 9 leaves 0 0
A. 85
B. 87
C. 88
To find the third quartile (Q3) of the temperatures represented by the stem-and-leaf plot, we need to understand how a stem-and-leaf plot works.
In a stem-and-leaf plot, the stems represent the tens digit of the data values, and the leaves represent the ones digit. The stem-and-leaf plot you provided can be interpreted as follows:
Stem 6 | Leaves: 9
Stem 7 | Leaves: 1, 2, 6, 7
Stem 8 | Leaves: 1, 4, 7, 9, 9
Stem 9 | Leaves: 0, 0
To find Q3, we need to determine the value that separates the upper 25% of the data from the lower 75% of the data. Since the data is organized in ascending order within each stem, we can start by finding the median (Q2) of the leaves in the stem 8 and 9.
Stem 8: 1, 4, 7, 9, 9 (odd number of leaves, so the median is the middle value)
Stem 9: 0, 0 (even number of leaves, so the median is the average of the two middle values)
The median of the leaves in stem 8 is the middle value, which is 7.
The median of the leaves in stem 9 is the average of the two middle values, which is (0 + 0) / 2 = 0.
To find Q3, we take the median of all the values greater than the median (Q2). In this case, the values greater than the median (Q2 = 7) are 9, 9, and 0.
So, Q3 is the median of 9, 9, and 0. Sorting these values in ascending order, we have: 0, 9, 9.
The median of 0, 9, 9 is the middle value, which is 9.
Therefore, the third quartile (Q3) of the temperatures represented by the stem-and-leaf plot is 9.
So, the answer is C. 88