I’m having an argument with another numerically literate person. We both saw a news site state that under no circumstances should you compare the median of one set with the mean of another.
It’s important to note what we mean by compare: no one is talking about constructing an hypothesis and test statistic to compare with a distribution. This is just a sort of layman, back-of-the-envelope rest of two distributions measured in dollars. One has a long trail sprinkled with upper outliers, the other does not and is presumably bell shaped. Also, I think we both agree that there are better ways to compare the two; the question is really about whether the news reporter should be chided for doing this mean-to-median comparison.