As we go out shopping for gifts this holiday season, given the state of the economy, a lot of people will be thinking about how to get the best value from their gift budget. A lot more people than usual, in fact, because as you’ll hear on TV or read online from time to time, the income gap in this country is exceptionally large.

It’s probably common knowledge that a large income gap means roughly a large difference between the richest and poorest income levels. But that’s not a very precise statement by itself. Suppose you have two tiny countries of six people each, and their incomes are distributed like this:

The difference between richest and poorest is the same in both countries, but the other values are significantly higher in Lolistan. We need to calculate something that takes into account everyone’s income, not just the extremes.

OK, how about the standard deviation? That’s the usual way to characterize how widely a bunch of numbers are distributed.