Saturday, July 2, 2011

An Interesting Tale of Statistics

I never realized that most babies are born later than expected. I foolishly thought that they would be dispersed normally about the expected 9 month date. But I got a lesson in statistics today from Tim Harford talking to his young daughter:
“I thought you wanted to talk about babies, my dear. By the way, did I ever tell you that you have more than the average number of arms?”

“But I have two arms.”

“Precisely. The average number of arms is less than two.”

“Don’t you mean fewer?”

“No. I don’t.”

“But everyone has two arms.”

“Not everyone has two arms. Most people do. The most common number of arms is certainly two. And more than 50 per cent of people have two arms, so the median number of arms is also two.

“But if you add up all the arms and divide by the number of people – which is what we tend to mean when we say “average” – you’ll find that the result is slightly less than two.”

“That’s silly.”

“No – that’s statistics.”

“Statistics are silly.”

“Statistics are not silly. But many people use them in a silly way.”

“They seem silly to me. So babies are a bit like arms?”

“A little bit. Some babies come months early, but no baby comes months late, and in any case the doctors have a tendency to get twitchy and whip the little tykes out when they’re a couple of weeks overdue.”

“But doesn’t that mean babies are likely to be early rather than late?”

“No: it means that a few babies are very early but no babies are very late. And this baby is not going to be very early, since it’s almost July and there’s been no sign of it yet.

“Anyway – if a few babies are very early and none are very late, then if you are trying to figure out a due date by adding up all the lengths of all these pregnancies, the very early babies will pull the average to the early side.”
I'm always delighted when people surprise me and show me that I didn't know something, especially when I thought I knew something!

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