Math Puzzler Of The Day

Updated Feb. 21 - see UPDATE section at the end of the article

Image credit: TEXample

Paul Krugman provides an excellent example of the difference between a mean average and a median average:

The three economists on this panel are all doing very, very well. Nonetheless, I’m pretty sure the panel’s mean wealth was three orders of magnitude larger than its median wealth.

Mean Versus Median, Illustrated

Mean average is the simple average of something. Add up the value of all the somethings, divide by the number of somethings, and that's the mean. Median average, on the other hand, is the value half of those somethings are lower than, and half greater than.

Here's an article that explains how to calculate these two values.

What's so important about these two concepts? People who are trying to tell you that the economy is just fine, and if you're not doing so well it must be your fault, often cite the fact that the mean average income in America, sometimes referred to as GDP per capita, is growing. The median average income, however, has shown little to no growth.

As differences go, it's like the difference between being comfortably well off, and being George Soros. Based on the discussions I'm occasionally unlucky enough to witness on this subject on television news shows, I'd say that not more than two Americans in ten understand this difference. This is both sad and another hint as to why our discussions of the economy are so nonsensical.

UPDATE (Feb. 21): Expat's comment on this article brought a couple of additional thoughts to mind. He wrote that he suspected that not more than two in ten Americans understand that there is a difference. He's probably right there, if only because if you understand there's a difference, you probably learned it at one time or another. That made me realize, though, that I hadn't done the obvious thing, which is to characterize what that difference actually means when it comes to describing the state of a national economy.

What that difference means is this:

* The mean income is how much income each of us would have on a yearly basis if that income were divided up evenly among all of us.

* The median income is the real measure of what the average person in an economy is making.

That's why understanding those two concepts is important.

For a great discussion of all of this, I'd recommend find a copy of Stephen Jay Gould's Full House: The Spread of Excellence From Plato to Darwin and read the chapter on baseball statistics, as well as the one on the modal bacter. The "modal" average is another concept in statistics - the particular type of something that has a particular value. Sometimes, it's a trivia question, like "what batting average, to a single percentage point, was most common among regular players in 1982?" Sometimes, though, it's important, as it is when one considers that bacteria are by far the most common life form on our planet. He also lectured on other implications of median averages.