Question

the box plots show a random sample of wait times for two rides at a water park. compare the wait times in the box plots. the median wait time for speed slide is 2 minutes longer than the median wait time for wave machine. the iqr for both rides is 6 minutes. if you go on both rides, can you be confident that your wait time for speed slide will be longer than your wait time for wave machine? yes. every speed slide wait time is more than every wave machine wait time. no. there is a lot of overlap in the two data sets.

Explanation:

Step1: Analyze the box - plots

Box - plots show the distribution of data. The median is the middle value of the data set. The inter - quartile range (IQR) is \(Q3 - Q1\).
For the "Speed Slide" and "Wave Machine" box - plots, we know that the IQR is calculated as \(Q3 - Q1\). But the key point for answering the confidence question is looking at the overlap of the data ranges.

Step2: Check for data overlap

If there is a lot of overlap between the two data sets (as indicated by the box - plot ranges), we cannot be sure that one value (wait time for Speed Slide) will always be greater than the other (wait time for Wave Machine). Just because the median of Speed Slide is higher than that of Wave Machine does not mean every value in the Speed Slide data set is higher.

Answer:

No. There is a lot of overlap in the two data sets.