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)
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 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.

Answer 1

IQR = Q3 − Q1. With 16 values, Q1 is the median of the first 8 values = (6.5 + 6.5)/2 = 6.5, and Q3 is the median of the last 8 values = (8.0 + 8.0)/2 = 8.0. So IQR = 8.0 − 6.5 = 1.5.

Correct choice: "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."