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 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.
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 spread of the middle 50% of a dataset. In this case, the middle half of the dataset (from the 25th percentile to the 75th percentile) includes shoe sizes from 6.5 to 8.0, which have a range of 1.5. Therefore, the IQR is 1.5.
Wrong
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.
The IQR, or Interquartile Range, is a measure of statistical dispersion, which describes how the values in a dataset vary around the median. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) in a dataset. In this case, the IQR is 1.5, which means that the shoe sizes for the middle half of the players (between Q1 and Q3) are within 1.5 shoe sizes of each other. This measure provides insight into the range over which the majority of shoe sizes for the players fall.
To find the IQR (interquartile range), you need to first order the shoe sizes from smallest to largest:
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.
Next, you need to find the values of the first and third quartiles:
- The first quartile (Q1) represents the 25th percentile, which is the median of the lower half of the data. In this case, Q1 is the median of the first 8 shoe sizes: (6.0 + 6.5)/2 = 6.25.
- The third quartile (Q3) represents the 75th percentile, which is the median of the upper half of the data. In this case, Q3 is the median of the last 8 shoe sizes: (8.0 + 8.5)/2 = 8.25.
To calculate the IQR, subtract the first quartile from the third quartile: 8.25 - 6.25 = 2.
Therefore, none of the given options accurately represents the IQR.
The correct description of the IQR would be:
"The IQR is 2. This means that the shoe sizes for the middle half of the players are within 2 shoe sizes of each other."