Compare Measures of Variation Quick Check

Question

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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 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 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 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.

Answer 1

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 variability that describes the range of the middle 50% of the dataset. In this case, the IQR of 1.5 means that the shoe sizes for the middle half of the players (from the 25th percentile to the 75th percentile) are within 1.5 shoe sizes of each other. This provides a more precise description of how the values in the dataset vary compared to just looking at the entire range of shoe sizes.