It is claimed that mean class size, as perceived by students, is always greater than a school's advertised average class size. This article gives a new quick proof, goes beyond previous inquiries to consider the perceptions of students taking multiple classes, and then develops a generalization for average population densities within a state or region. As a bonus, the discussion invokes famous inequalities by Chebyshev and Cauchy.
The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. CMJ publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.