Question

The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.

Which drive-thru is able to estimate their wait time more consistently and why?

Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range

Answer 1

Burger Quick is able to estimate their wait time more consistently because it has a smaller interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data, which is represented by the box in the box plot. A smaller IQR indicates that the data is more tightly clustered around the median, which in turn indicates that the wait times at Burger Quick are more consistent. The range, which is the difference between the maximum and minimum values in the data set, is not as informative as the IQR for comparing the consistency of the wait times, as it is influenced by outliers. Therefore, the correct answer is: Burger Quick, because it has a smaller IQR.

Answer 2

Super Fast Food is able to estimate their wait time more consistently because it has a smaller interquartile range (IQR), which means that the middle 50% of the wait time data is more tightly clustered around the median. A smaller range alone does not necessarily indicate consistency in wait time estimation, as outliers can greatly affect the range.