A Teaching Moment on Numeracy

(Photo: John Foxx)

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?

  1. 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.
  2. 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.
  3. 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.
  4. 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.


This article echoes precisely my sentiment whenever big numbers are thrown out there to illustrate a point. Especially points 1, 2 and 3. Also what irritates me is that many people like those who will read James B. Stewart will assume his statement true just because they see him as a credible source. Heck, the entire country thought Iraq had WMD's just because the Bush Administration fed us a few BS satellite pics, but I'm digressing.
My point is go check the facts, be it numbers or statements.


"we know" is also a loaded preamble- auto inclusives to knowledge are often rhetorical manipulators regardless of (true) content

robyn ann goldstein

well, when there's nothing better, a false debt ceiling is better than no ceiling at all. But I still say- we need to pay our bills. China won't be happy if we do. But wow, imagine a debt free America. Sell bonds if we have to do so. What is the problem. I see it now. a false understanding of Post-industrial society as functional without producing anything. In a way, am I any different? Produce or perish.


I think that keeping your units constant is key in giving perspective when dealing with really large or really small numbers. Going from million to billion, almost interchangeably, can be very misleading. I feel XKCD has a comic that perfectly exemplifies this point, as usual.



Good points, but I might choose to avoid the NBA analogy, due to basketball's being primarily an urban game, and murder being associated with urban settings. It would sound different if you made a baseball or soccer analogy. It would sound different if you said "imagine all the people attending a Broadway show tonight - on average one of them will be murdered this year." It would sound different if you tied the number to the SXSW festival. Context matters.


"We know how many murders are committed each year..."

But - and I'm sure every reader of murder mysteries would argee - we don't know how many murders are committed. We know how many deaths are reported and labeled as murders in the crime statistics. Some fraction (one hopes a small one) of those are really natural & accidental deaths that were mislabeled, another fraction of deaths were filed as natural/accidental (or not reported at all), because the murderer took sensible precautions...


We do math all day here at work. If we are wrong, we lose money...sometimes lots of money. Our best skill is that we can smell a bad number. To some degree, this is a learned skill but mostly, I think, it is a skill you are simply born with.

The two guys I work with are amazing at "smelling a rat". They don't teach this at school very well and most people just write down whatever the calculator says.

One guys here still complains about 6th grade when the teacher would mark down his score for not "showing his work" despite getting the correct answer while rewarding those with absurdly wrong answers because they "showed their work" properly.


I'm off to lunch.

I'll be back in three thousand seconds.

Eric M. Jones

I support an act of congress to make the millions, billions, trillions, NOT rhyme.

The only way of understanding a really big pile of dollars is “Opportunity Cost”; that is, what you could buy with the money.

What could one do with a billion dollars? A billion dollars is more than all the Alaskan gold mined in 2010— a cubic METER of gold.

Just five percent of that billion dollars ($50 million) would get you: A lifetime lease on a Gulfstream G450 at your beck and call. A home, condo or apartment in ten major exotic destinations, with a (leased) luxury fleet of cars at each, a coterie of servants to follow you around, memberships in every exclusive club, all you could possibly eat, wear, play with and see for a lifetime. And Hell, throw in a yacht. Then you could sail around sipping expensive wines imagining ways to spend the other $950-million dollars.


Good topic, but bad example. “We know how many murders are committed each year — 1,318,398 in 2009.” Who would really believe such an absurd statement. My original thought was this was a number for the entire world. The point got lost. I would also have to dissagree with point one, there is nothing wrong with numbers. Just provide the numbers in an intuative way. Numbers are provide a higher level of proof, compared to words.


Really? How to avoid being wrong when using numbers... don't use numbers. This hardly seems like the kind of advice I expect from the Freakonomics blog. Point 3 and 4 are good advice. Point 1 and 2 just seem like they are saying, readers (and writers) don't understand any math (or really how to count). So, I guess that settles it, people aren't good at math so we shouldn't report numbers, just say "a lot" or "not many" and that way we'll never have to actually look-up or confirm anything.


I use those same concepts in my 8th grade classroom all the time! Glad I'm ahead of the curve on something.


"...1 in 230 people is killed each year."

Actually, he implied that this many people are murdered, not just killed. I think that's an important distinction. Thanks for this article -- very important things to remember.


Given the title of his book, do you think that maybe, just possibly, Mr. Stewart was making an ironical point?

Just wondering.


"Statistics are like ladies of the night. Once laid out...you can do anything with them." [Mark Twain, i believe]

It all comes down to the ideology a person subscribes to because there are plenty of numerical and semantical arguments on every side. of course, ideology is still subject to logic and practicality.

This blog for example produces numeorus (so called solid)numbers and arguments every week and yet every reader leaaves with his/her own conclusions (from keynesians to austrians).
Raw data is incomprehensive; therefore, we always need someone (who is always subject to a bias) to polish them.

Peace out, yo!

Mike 2

I'll disagree with point 1, for argument's sake.

15,241 murders were committed last year - that's a value-neutral statement.

But if I say "a lot of murders were committed last year", I've introduced my values. I'm saying that I think that is a lot of people. But what if it was the lowest number in 30 years, or a decline of 50% from the previous year? It would be easy to criticize me for trying to hide a decline in murders by talking words instead of numbers.

How you choose the words is important. If murders are up 3% over last year, do you say they "rose slightly" or "skyrocketed"?

My point is that if you're going to use words instead of numbers, it gets much easier to introduce your values into the discussion, and for your core point (whatever that it) to get lost.

Justin Trombley

I find it a little funny that in pointing out how not to make a mistake it seem that link mistakenly links to the MLB attendance not the NBA. I know a little blog link mistake is nothing like a published book where you drop wrong numbers. Everything you said sounded like great advise I just found it funny is all.


That number may be reasonably accurate for yearly murders in the entire world. It is rather America-centric to assume he is talking about the US (I realize the word America appears in the book title).

Reminds me of the claim heard on the news that "50 thousand people died in the Vietnam War." Sorry, over 3 million people died in the war, but I guess many of those don't matter.


There really has to be both numbers and words.
For instance,
I got a 93 on the test. (good)
Out of 1000 points. (bad)
It was the highest score in the class. (good)
The lowest score was 92 (bad)
There were three students in the class (bad)
You get the idea.


Got into a discussion with a newly-minted family member over the oft-recited Limbaughism that one in ten Moslems are terrorists. Uncle Conservative made that statement and I asked, so you believe there are three hundred million terrorists out there? One for every person in the United States? Why haven't they just invaded? Mother-in-Law Liberal and New Wife hustled Uncle Conservative out of the room before it could go any farther. People make these glib statements using numbers and the gullible never question them, never give them the sniff test, never bother to learn that one in ten of three billion is the population of the United States.