John Allen Paulos in Scientific American:
The number of friends we have is typical of many situations in which the average deviates from individuals’ experience. Another is class size. Let’s imagine a small department offering three courses for the semester. One is a survey course with 80 students, one an upper-level course with 15 students, and one a seminar with five students. Now what is the average class size? Clearly, it is (80 + 15 + 5)/3, or 33.3 students. This is the number the department is likely to publicize.
But once again, let’s adopt the perspective of the average person and reexamine these numbers. Eighty of the 100 students find themselves in a class with 80 students, 15 find themselves in a class of 15 students, and five in a class of five students. Thus, the average student’s class size is (80 × 80 + 15 × 15 + 5 × 5)/100, or 66.5 students. This number is less likely to be publicized by the department.
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