The Inspection Paradox

 Suppose you ask college students how big their classes are and average the responses.  The result might be 56.  But if you ask the school for the average class size, they might say 31.  It sounds like someone is lying, but they could both be right.

Allen Downey

The reason is that there are obviously classes with more than 31 students, and some with less. That means that more students are in larger classes, so a student chosen at random will report being in a class with more students than average.