You are great at baseball and you are able to play professionally. However, you are not a "star."
What professional team would you rather play for? And, why?
Mean versus Median.
Because baseball salaries tend to be skewed data, using salaries from professional teams is a great way to introduce the ideas that (a) mean is not always the best measure of center and (b) median and mean are only similar when the data is symmetric.
I select various baseball teams—teams that I like, teams that my class likes, and teams that I know have overly, high-paid players. I give each group a different team and ask them to examine the teams. Posing the question above. Of course, students calculate the mean.
I then ask the students if there are other ways to compare team—eliciting other measures like median, minimum, maximum. Eventually, I encourage students to make box-and-whisker plots. When we try to compare the box-and-whisker plots at the document camera enviably we use different scales for our box-and-whisker plots and a discussion about a common scale emerges. Then, we make a class poster with a common scale (I come prepared).
Once the group poster of different box-and-whisker plots is made, there is great discussion about spread and quartiles. Students use this reasoning to decide what team they would rather play for.