No, statistics are not silly, but their users . . .

2nd July, 2011

“Dad, when is Mummy’s new baby going to come?”

“Nobody knows, my love. We’ll have to see when the baby decides to come out.”

“But everybody talks about babies being early or late, like buses.”

“Buses are a little different from babies – you wait ages for a bus and then several come along at once, and that’s definitely not the aim here.”

“But babies can be late, like buses?”

“Yes, they can be late.”

“So if they can be late, there must also be a time when they are supposed to arrive.”

“That’s right. The new baby is due on the 15th of July – that’s about two weeks away.”

“But it might be late.”

“It might be late, yes. Or it might be early. But the truth is it will probably be late. You were late and so was your sister.”

“How can you say it will probably be late? Aren’t babies, on average, on time?”

“I’m not sure how you can make that claim. Buses are certainly not on time, on average. They are systematically prevented from being early but cannot help sometimes being late – so on average, they are late.”

“Bus timetables are different. Everybody knows the bus timetable is when the bus is supposed to arrive, not some historical record of when the bus has actually tended to arrive.”

“Good point. In fact, that gives me an idea. Maybe we should rewrite bus timetables based on historical data.”

“But Dad, don’t people want to know the earliest time at which a bus will arrive, rather than the average time?”

“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.”

“Is that what happens?”

“Yes. Here – let me consult my copy of The Tiger That Isn’t, by my friends Michael Blastland and Andrew Dilnot.”

“Is it a book about a tiger?”

“Obviously not – since the tiger isn’t.”

“Is it a book about babies?”

“No. It is a book about numbers. Due dates in the UK are calculated by adding 280 days to the date of the mother-to-be’s last period.

“And Blastland and Dilnot say that 280 days is indeed the average. But in fact 50 per cent of mothers wait at least 282 days. And most commonly, the baby is actually born after 283 days. In other words, the typical baby is born two or three days late.”

“But if the typical baby is three days late, is it really late at all?”

“You tell me, my love. I’m just an economist. The doctors say that it is.”

“Doctors are silly.”

“Perhaps they are, my love – at least, sometimes. But I am sure doctors would say that economists are sometimes silly, too.”

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