Compare Measures of Variation Quick Check
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Question
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 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 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 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.
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.
Explanation: The IQR (Interquartile Range) is a measure of how spread out the data is in the middle half of the dataset. It is calculated by finding the difference between the third quartile (Q3, the 75th percentile) and the first quartile (Q1, the 25th percentile). In this case, Q3 is 8.5 and Q1 is 7.0, so the IQR is 8.5 - 7.0 = 1.5. This means that the shoe sizes for the middle half of the players (from Q1 to Q3) are within 1.5 shoe sizes of each other.
The correct answer 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.
Explanation:
The IQR stands for Interquartile Range, which is a measure of variation that describes the spread or dispersion of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
In this case, the IQR is 1.5. This means that the shoe sizes for the middle half of the players (between the 25th and 75th percentiles) are within 1.5 shoe sizes of each other. It provides an understanding of the range in which the majority of shoe sizes fall, indicating how the values of the dataset vary within a single number.