Question

you are planning to visit a theme park with friends. since you will have a limited amount of time at the park, you do some research on wait times for the rides. the box plots show a random sample of wait times for two of the rides. what can you infer from looking at the medians of the samples? the typical wait time for free flyer is shorter than the typical wait time for steel thunder. if you go on both rides, can you be confident that your wait time for free flyer will be shorter than your wait time for steel thunder? yes. the wait times for free flyer are all less than every wait time for steel thunder. no. there is a lot of overlap in the two data sets.

Explanation:

The median of a box - plot represents the middle value of the data set. If the median of Free Flyer is to the left of the median of Steel Thunder on the number line (which is the case here as the median of Free Flyer is less than that of Steel Thunder), it means the typical (median - based) wait time for Free Flyer is shorter. However, for the second part, just because the median of one data set (Free Flyer) is less than the median of another (Steel Thunder) does not mean that every value in the first data set is less than every value in the second. There is an overlap in the ranges of the two box - plots (the whiskers and boxes cover some of the same time intervals on the number line).

Answer:

For the first part: The typical wait time for Free Flyer is shorter than the typical wait time for Steel Thunder.
For the second part: No. There is a lot of overlap in the two data sets.