Two common measures of the location of a probability distribution are the mean and the median. While generally, they are quite different things, some familiar distributions have their mean and median at the same point (all such distributions are symmetric, and

*vice versa*).
The mean of a distribution, as we all know, is its average, while the median is the point at which the amount of probability mass to one side is the same as the amount on the other side. Upon hasty consideration, these definitions can appear to denote the same thing, and so confusion between the two concepts is common. Annoyingly, my own PhD thesis contains a sentence

^{1}that explicitly confuses the mean for the median (and furthermore, none of the half dozen eminent scientists whose job it was to assess my thesis (who otherwise all did an excellent job!) reported noticing this blunder).
Confusion between the mean and the median is highly analogous to a difficulty experienced by many young children when they try to balance asymmetric blocks on top of one another, as has been reported by cognitive scientist Annette Karmiloff-Smith

^{2}.