Who's Counting: It's Mean to Ignore the Median

Aug. 6, 2006 — -- Believe it or not, the difference in the way the Democrats and Republicans react to the performance of the U.S. economy is clarified by a mathematical distinction studied in elementary school. The distinction is between the mean, which the Republicans emphasize, while the Democrats prefer the median. Before turning to the economy, let me review a little fourth-grade arithmetic.

The mean of a set of numbers is simply the average, and it is obtained by adding the numbers in the set and dividing by how many there are. The median of a set of numbers is obtained by listing the numbers in the set in ascending order and locating the middle number in the list. The same set of numbers can have a mean and a median, which differ significantly.

A real estate agent, for example, informs you that the mean price for a house in a certain neighborhood is $500,000 and implies that there are many houses above that price in the neighborhood. Not necessarily. If most of the houses sell for somewhere between $100,000 and $200,000, and there are a few multimillion dollar mega-mansions, the mean price of a house in the neighborhood might well be $500,000, even if the median is, say, $160,000.

Or a salesman tells you that the median commission on the nine sales he made that week is $80 and suggests that he therefore made $720 on these sales. Maybe, but he could have made millions of dollars on these sales if one of the sales was enormous, or he might have made little more than $400 if four of the sales were near $0 and the other five were $80 or slightly more.

The relevance of this distinction is apparent in the just-released figures on the U.S. economy for 2004, the latest year for which there is complete data. The Republicans chortle that the economy grew at a healthy rate of 4.2 percent. (It's slowed since then.) The Democrats point to data from the Census Bureau for the same year (and earlier as well), indicating that the real median family income fell and that poverty increased.