The Paradox of Averages

A possible problem arises when we note that the average number of courses taken by all eight people is smaller than the average number of courses taken by those who took at least one course of a particular type. That is, if we look only at the three people who took at least one math course, we find that the average number of courses they took (8.33) is bigger than the average number of courses taken by all eight people (5.75).

OK, you say, maybe there's something special about those people who take math courses that explains why they take more courses on average.

But if we look only at the four people who took at least one science course, we find that the average number of courses they took is also bigger (8.25) than the average number of courses taken by all eight people. Again, we might think there's something special about those people who take science courses that explains why they take more courses on average.

The full paradox appears after we finish checking those who took at least one social science or one humanities course and discover that the same phenomenon holds for them. If we look at those who took at least one course of type X, whatever X is, we will find that the average number of courses taken by this group is higher than the average number reported by the whole group.

It seems that using this particular method of reporting people's course loads can sometimes justify a Lake Wobegon-style boast that those who take any particular type of course take an above average number of courses.

This odd result may be of use to spin doctors in politics or education.

Professor of mathematics at Temple University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on ABCNEWS.com appears on the first day of every month.

Page
  • 1
  • |
  • 2
Join the Discussion
blog comments powered by Disqus
 
You Might Also Like...