I once edited a book review in which this sentence appeared (details have been changed to protect the guilty): "Oglethorpe Carrothers was one-third journalist, one-third statesman, one-third war hero, one-third humanitarian, and one-third playboy." Granted, math isn't my strong suit, but I know enough to raise an eyebrow when I meet five-thirds of a Carrothers.
Like that reviewer, many people are more concerned about the sound of their words than the sense of their numbers. The words read well, but the numbers don't add up. Beware of any figures you haven't checked and double-checked. Count on your fingers if you must, but be sure the math makes sense.
What do you make of this sentence? The stock price jumped 200 percent in less than an hour, rising to $50 from $25. Something's wrong here (even if you got in on the stock early). Do you see why?
When you start with $25 and you increase that by $25, you've doubled the original figure, to $50. But that's a jump of only 100 percent, the original number increased by itself once. When $25 goes up 200 percent, it increases by itself not once but twice—that gives us the original $25, plus $25 and another $25, for a total of $75.
Goofy percentages whiz past us every day. They routinely appear in newspapers, TV broadcasts, and magazines because nobody stops to count.
Doubling, tripling, and quadrupling are all clear enough: a number is multiplied by two, by three, by four. But tossing in percentages leads to trouble. A number that's doubled goes up 100 percent, a number that's tripled goes up 200 percent, a number that's quadrupled goes up 300 percent, and so on. Go figure.
This is a case where being right isn't necessarily the answer. If there's an alternative, avoid using percentage increases of more than 100, especially big round ones that look wrong even when they're right. It may be correct to write, Scalpers sold the $10 tickets for $50, a 400 percent increase, but this is better: Scalpers sold the $10 tickets for $50, five times the original price. When there's no better way, at least make sure the figure is right: The police arrested 156 scalpers this year, a 140 percent increase from the 65 arrested last year.
Never use decreases of more than 100 percent, however, unless you're writing about mathematics. A 100 percent drop gives you zero, so any greater decrease would leave you with a negative number. Outside of math class, your chance of being right is less than zero.
Two times two is four, and that will never change, at least not in our times. But times is tricky when you're writing about numbers. What do you make of the calculation here? Mort owns two Chihuahuas but Rupert owns eight, or four times more.
If that looks right to you, look again. Rupert actually has three times more Chihuahuas than Mort. Think of it this way: Rupert owns six more than Mort. And that's three times more than Mort's two, not four times more. Chihuahuas don't multiply that fast.
We run into trouble using the expression times more when we forget that we're adding the times calculation to whatever it's more than. The problem is so widespread that I'd suggest ducking it altogether. Why not drop the more and use times as many or times as much? A math teacher—and an English teacher, too—would give you an A for this effort: Mort owns two Chihuahuas, but Rupert owns eight, or four times as many.
We also go wrong when we write that a number is umpteen times less than another: Baby Leroy weighs twenty pounds, five times less than his mom, who weighs a hundred.
The problem is the same; it's just going in the other direction. You could say that the baby weighs four times less than his mom (think of it this way: his weight is eighty pounds less, or four times twenty less, than his mom's). But even that wording gives me a headache.
Again, I recommend copping out. Drop the times less and rephrase the sentence, using as many as or as much as instead: Baby Leroy weighs twenty pounds, a fifth as much as his mom, who weighs a hundred.
The most common times problems involve more and less. But the same principle applies whenever you use numbers to compare things. Instead of saying, So-and-so is x times richer than what's-his-name, make it: So-and-so is x times as rich as what's-his-name (or as tall as, as old as, and so on).
If you take my advice, you' ll find it comparatively easy, more or less.
How many sheep are in this fold? Babe's flock of ten sheep increased threefold last year. No, the answer isn't thirty, although that's probably how most people would interpret the sentence. The answer is forty—the original ten, plus three times that number.
And that's the problem with using fold to say how much something has increased. Attaching fold to a number is just another way of saying times, and it can be just as confusing. Even if you get it right, you'll probably be misunderstood.
The solution? Don't use fold to say something has doubled, tripled, or quadrupled. Just say that it has doubled, tripled, or quadrupled: Babe's flock of ten sheep tripled last year. Or you could make it: Babe's flock of ten sheep increased to three times as many last year. This solution is definitely preferable with larger increases. If Babe ended up with 150 sheep, make it: Babe's flock of ten sheep increased to fifteen times as many last year.
By the way, don't use by when you mean to. They're not the same, not by a long shot. If Babe's flock had increased by fifteen times as many, he'd have 160 sheep—the original ten, plus fifteen times as many. Way to go, Babe.
As if fold weren't confusing enough, it's even woollier to say, Babe's flock often sheep increased three times last year. You run into the same problem, and another besides: You might mean that three lambs joined the flock last year, or that the flock increased on three separate occasions.
All right, we've counted enough sheep. One more thing before I fold. Whatever you do, never use fold to describe a decrease. I recently read that a country's food supplies had fallen sixfold. If you know what that means, please explain it to me.
As I've said, I'm not a whiz at math. I make it a practice to check my figures two times, maybe three, with even the most elementary arithmetic. If I get the same number twice, I go with it. But numerically clumsy though I am, I once worked at the Wall Street Journal, where every number had to be perfect. If I can get my numbers straight, so can you.
A tip that I learned as a business journalist has stuck with me over the years. It's worth passing on, and it's useful for writing about more than money.
When a number changes, whether it's going up or going down, it moves from one point to another. So we're tempted to write things like this: As El Niño arrived, the temperature rose from 5 to 10 degrees.
But just how warm did it get?The phrase from 5 to 10 could be read in two ways. It might mean the temperature started at 5 degrees and rose to 10. Or it might mean the increase was between 5 and 10 degrees, so the temperature might have ended up at 40, for example, after beginning somewhere in the 30's.
It's easy to get around this problem. Just put the to ahead of the from: As El Niño arrived, the temperature rose to 10 degrees from 5. Or if you do want to describe an approximate increase, make it: As El Niño arrived, the temperature rose between 5 and 10 degrees.
If you keep to in front, your readers will know where you're coming from.
I can't promise this problem will be on the SAT's, but it sure comes up a lot: If one in every ten boys starts school early, and three in ten girls, does that mean four out of ten children start school early?
No. If you got it wrong, here's a little remedial math.
First of all, you can't mix the proportions unless there are equal numbers of boys and girls. Assuming that's the case, you don't add the statistics; you average them. If one in ten boys and three in ten girls start school early, then two in every ten children start early.
The principle is the same with percentages. If 8 percent of American men and 12 percent of American women are overweight, that doesn't mean 20 percent of all American adults are overweight. The answer is 10 percent, again if we assume there are equal numbers of men and women. You don't add the two percentages; you average them. (Remember that if the groups aren't the same size, averaging won't work.)
As with so many other things, the truth lies in between.
A lot of us can't tell our ups from our downs. If we're comparatively impaired, we might call something a "decrease" when in fact it's an increase—but an increase that's smaller than average, or smaller than last year's, or smaller than expected, or whatever. A lesser increase is still an increase, not a decrease.
Journalists are often guilty of this mistake, especially when they write about budgets. A story on school spending might refer to a "decrease" in maintenance costs when the amount in fact increased—but the increase was smaller than the one expected. As a result, we get a story about "budget cuts" when the budget has actually grown. Sometimes less really is more.
I'll bet the average person doesn't know the difference between average and mean, median and norm, or any of the combinations thereof. The average dictionary may not be of much help, either. Not all dictionaries give precise mathematical meanings.
Imagine you're taking a seminar in desktop publishing. The five students in the class get these scores on their midterm exams: 60, 84, 87, 94, 100. (All right, you're the one who gets 100.) Here's how to find the average, mean, median, and norm.
•The average is 85: the sum of the scores (425) divided by the number of students (5).
• The mean, also known as the arithmetic mean, is 85: same as average. (Some dictionaries and usage guides define mean in a looser sense, as the mid-point between extremes.)
• The median is 87: the score that falls in the middle when the numbers are arranged by size. If there's an even number of scores, add up the two in the middle and divide by two.
•The norm is in the 80 's: a less precise term, it's sometimes used to indicate average or median or just "normal"; avoid it when you want to be exact.
If you can remember all that, you're way above average.
Writers who are careless with figures are on thin ice. What's the weak spot here? Hundreds of ice fishermen aren't licensed in Minnesota.
If you don't see what's wrong, here's a clue. Not all ice fishermen are in Minnesota. No doubt there are many thousands, from Maine to Siberia, who aren't licensed to fish in Minnesota. Here's a better way to say it: Hundreds of ice fishermen in Minnesota aren't licensed.
When you write with numbers, be sure your wording isn't misleading. Readers may guess what you mean, but why should they have to? If there's any ambiguity, rearrange the words, as in the example above, or add any information that may be missing. Something's missing here: S even out of ten people are robbed by someone they know.
I doubt it. Most people are never robbed by anyone, strangers or otherwise. Say it this way: Seven out of ten people robbed are victims of someone they know.
Statistics can be treacherous. As Disraeli supposedly said: "There are three kinds of lies: lies, damned lies, and statistics."