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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 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 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 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.

1 answer

To calculate the Interquartile Range (IQR) for the given shoe sizes, we first need to determine the first (Q1) and third quartiles (Q3) of the dataset.

The shoe sizes provided 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

  1. Order the data (already in order).

  2. Calculate Q1 and Q3:

    • The data has 16 values. The positions of Q1 and Q3 can be found as follows:

      • Q1 is the median of the first half (8 values): 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5

      • The median of this half, 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 (8 values): 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0

      • The median of this half, 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.

Now we can choose the correct response:

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.

Therefore, 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.