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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 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.
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.

1 answer

To calculate the Interquartile Range (IQR), we first need to determine the first quartile (Q1) and the third quartile (Q3) of the dataset.

  1. Arrange the data in ascending order (which is already done):

    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

  2. Find Q1 and Q3:

    • Q1 is the median of the first half of the data. The first half includes the values: 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, which has 8 values. So, Q1 is the average of the 4th and 5th values:

      • (6.5 + 6.5) / 2 = 6.5

    • Q3 is the median of the second half of the data. The second half includes the values: 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0, which also has 8 values. So, Q3 is the average of the 4th and 5th values:

      • (8.0 + 8.0) / 2 = 8.0

  3. Calculate the IQR:

    IQR = Q3 - Q1 = 8.0 - 6.5 = 1.5

Based on this calculation, the IQR is 1.5.

The correct interpretation would be:

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.

So, 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.