Sunday, August 27, 2006

Statistics, Statistics!

Most of us, at one time or another, have heard something like this: "in the Middle Ages, the average life span was shorter than forty years; today, life expectancy often reaches as high as the mid seventies."

Makes us sound pretty cool, right? I mean, with all our modern technology and science, and good medical care, we're much better off!

Well, not really.

Notice the slightly different wordings: "average life span" and "life expectancy". These are, to statisticians, two very different things.

Average life span is simply the arithmetic mean of a group of human beings, for example, those living in Europe in the Middle Ages. Some of them died as small babies, others lived to be 100 years old or more, and most were between those two extremes. Add them up, divide, and you have the average. You learned to do that in some math class.

But "life expectancy" is a little trickier. For example, the generation of Americans who fought World War Two is now over eighty years old. We look around, and see many of them still living; others have died only recently, having made it into their seventies. And so we say that this generation had a pretty good "life expectancy". But their average life span was much shorter. We forget about the hundreds of thousands who actually died in the 1940's, fighting in the Pacific against Japan. When they are factored into the group, we find that the average life span is much shorter than the life expectancy. Remember, many of those soldiers who died were under twenty years of age.

Your life expectancy is defined, roughly, as how long you can expect to live if you have already made it to a certain age, say 20 or 30, and if there are no major unforeseen catastrophes, say like a war or an earthquake.

It's not meaningful to compare a modern life expectancy to a medieval average life span. That's comparing apples to oranges.

Given that the modern life span is shorter than the modern life expectancy, maybe we're not so much better off than those folks in the Middle Ages after all.