Question

Question 7(Multiple Choice Worth 2 points)

(Appropriate Measures MC)

The table shows the number of goals made by two hockey players.


Player A Player B
1, 4, 5, 1, 2, 4, 5, 5, 11 1, 2, 1, 3, 2, 3, 4, 1, 8


Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with a range of 10.
Player B is the most consistent, with a range of 7.
Player A is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with an IQR of 2.5.

Answer 1

(d) Player B is the most consistent, with an IQR of 2.5.

Explanation:

Given these numbers of goals, you want to know which player is most consistent, and the best measure of that.

• A: {1, 1, 2, 4, 4, 5, 5, 5, 11}
• B: {1, 1, 1, 2, 2, 3, 3, 4, 8}

Variability measures

The variability measures we're to consider here are range and IQR.

The range is the difference between the maximum and the minimum:

• A: 11 -1 = 10
• B: 8 -1 = 7

The smaller range indicates player B is more consistent.

The IQR is the difference between the upper and lower quartiles. In each of these 9-element data sets, those quartiles will be the average of elements 2 and 3, and the average of elements 7 and 8 when the data is in order.

• A: ((5+5) -(1+2))/2 = 3.5
• B: ((3+4) -(1+1))/2 = 2.5

The smaller IQR indicates player B is more consistent.

Outliers

In each case, the maximum data value is more than 1.5 times the IQR above the upper quartile value, so can be considered an outlier. The outlier has a direct effect on range, so range is not a good measure of variability.

Player B is the most consistent, with an IQR of 2.5, choice D.

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Additional comment

If the outlier is excluded from each data set, the IQR for player A remains the same at 3.5. The IQR for player B drops to 2.0.

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