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 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 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 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. pick.

Answer 1

To find the interquartile range (IQR) for the given dataset, we first need to find the first quartile (Q1) and the third quartile (Q3).

The dataset sorted in ascending order is:
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

There are 16 values in the dataset.

First, calculate the positions of Q1 and Q3:
- The position of Q1 is \( (n+1) \times \frac{1}{4} = 17 \times \frac{1}{4} = 4.25 \)
- The position of Q3 is \( (n+1) \times \frac{3}{4} = 17 \times \frac{3}{4} = 12.75 \)

Since positions 4.25 and 12.75 are not integers, we need to interpolate between the values in those positions.

For Q1:
- The value at position 4 is 6.5
- The value at position 5 is 6.5
- Interpolating between these gives \( Q1 = 6.5 \)

For Q3:
- The value at position 12 is 8.0
- The value at position 13 is 8.0
- Interpolating between these gives \( Q3 = 8.0 \)

Now, calculate the IQR:
\[ IQR = Q3 - Q1 = 8.0 - 6.5 = 1.5 \]

So, the correct choice 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."