To find the interquartile range (IQR) of the shoe sizes for the varsity field hockey team, we first need to find the first quartile (Q1) and third quartile (Q3) of the dataset.
First, we need to arrange the 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
Q1 is the median of the lower half of the dataset, which is the median of the numbers to the left of the overall median. In this case, the numbers to the left of the median are 6.5, 6.5, 7.0, 7.0, so Q1 = (6.5 + 6.5) / 2 = 6.5
Q3 is the median of the upper half of the dataset, which is the median of the numbers to the right of the overall median. In this case, the numbers to the right of the median are 8.0, 8.0, 8.5, 8.5, so Q3 = (8.0 + 8.0) / 2 = 8.0
Now, we can calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1
IQR = 8.0 - 6.5
IQR = 1.5
Therefore, the interquartile range (IQR) of the shoe sizes for the varsity field hockey team is 1.5. This measure of variability describes how the values of the dataset vary with a single number by indicating the range in which the middle 50% of the data falls. In this case, it shows that the shoe sizes of the players in the team vary by 1.5 sizes in the middle 50% of the dataset.
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?
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