A Teaching Moment on Numeracy
It’s an embarrassing episode. The opening sentence of James B. Stewart’s Tangled Webs: How False Statements Are Undermining America is:
“We know how many murders are committed each year — 1,318,398 in 2009.”
But this is false. As Jeffrey Rosen notes in a savage New York Times review, there were 15,241 murders in 2009. The cited number isn’t just wrong, it’s wrong by two orders of magnitude. Where did the 1,318,398 come from? It’s the number of violent crimes, which includes robbery, rape and assault. And only a small proportion of all violent crimes — a little more than 1 in 100 — are murders.
And so this provides a useful teaching moment for thinking about numeracy. How can you avoid such errors?
- Don’t use numbers when words will do. The rhetorical point that Stewart was trying to make is simply that there are a lot of murders. Too many. You don’t need numbers to say this.
- Don’t use numbers that are hard to comprehend. We have everyday experience in thinking in dozens. But we’re hopeless when it comes to millions, billions, or at the other extreme, tiny fractions. For instance, no one ever made the mistake of saying there are 12,000 eggs in a typical carton. But plenty of journalists confused the $700 billion TARP bailout, describing it as a $700 million plan.
- Scale matters: Big (and small) numbers only make sense relative to something else. Is 15,241 murders a lot for a country the size of the U.S.? Find a scaling that gives this some meaning (and avoids the artificial precision of 5 significant figures). Perhaps: Last year around 1 in 20,000 people were murdered. But how can you get your reader to picture 20,000 people? Easy, it’s roughly the number of people who attend a typical MLB game.To over-simplify: Look around an average NBA basketball stadium. If the crowd is representative of the streets, someone in this crowd will be killed this year.
- The laugh test: When you really think about your number, does it seem plausible, or is it laughably wrong? My basketball stadium analogy conveys the true extent of the U.S. homicide problem. If Stewart had followed this advice, he would have seen that his wrong number implied that 1 in 230 people is killed each year. Straight away he would realize that he isn’t grieving the murder of one of his Facebook friends every year or two.