To calculate the Interquartile Range (IQR) of the given shoe sizes, we need to determine the first quartile (Q1) and the third quartile (Q3).
The given shoe sizes in ascending order:
5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0
1. Find the median (Q2) of the dataset.
- There are 16 values, so the median is the average of the 8th and 9th values.
- The 8th value is 7.5 and the 9th value is also 7.5.
- Therefore, the median (Q2) is 7.5.
2. Find Q1, which is the median of the first half of the dataset (excluding the median):
- The first half is: 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5.
- The median of the first half (Q1) is the average of the 4th and 5th values:
- The 4th value is 6.5 and the 5th value is also 6.5.
- Therefore, Q1 is 6.5.
3. Find Q3, which is the median of the second half of the dataset (excluding the median):
- The second half is: 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0.
- The median of the second half (Q3) is the average of the 12th and 13th values:
- The 12th value is 8.0 and the 13th value is also 8.0.
- Therefore, Q3 is 8.0.
4. Calculate the IQR:
- IQR = Q3 - Q1
- IQR = 8.0 - 6.5 = 1.5
Therefore, the correct response is:
The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.
The shoe sizes for a varsity field hockey team are: 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0 Which of the following is the IQR and explains how this measure of variability describes how the values of a dataset vary with a single number? (1 point) Responses The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other. The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other. The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other. The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other. The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other. The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other. The IQR is 3.5. This means that the shoe sizes for the middle half of the players are within 3.5 shoe sizes of each other.
1 answer