Lately I've been hearing and reading statistics that are communicated in wording that, frankly, confuses me. Forgive me for not citing specific instances, but I can give a hypothetical statistic that exemplifies the kind I'm referring to:

Comparing the number of tax returns the IRS audited in 2002 and 2010, the number of unlucky folks who had their returns audited in 2002 was ten times fewer than the number in 2012.

There is something about that wording that bothers me, and I'm not sure why.

After a fruitless search on the internet using numerous combinations/permutations of words and phrases such as "X times fewer," "X times less," "mathematical expressions of 'times fewer' as opposed to 'a fraction fewer,' or 'a fraction less,'" and more, I came up empty. Perhaps this question is more appropriate on a math website, but in the off-chance members of EL&U might give their imprimatur to this question, here goes:

Here's a second hypothetical example. Is it grammatical—not to mention mathematical—to say the following?:

There are ten times fewer pollinating honeybees worldwide today than there were in 1912. [Though this is a made-up statistic, there has been a dramatic reduction in the number honey bees in America of late!]

Should not the expression be:

There are one-tenth fewer honeybees worldwide today than there were in 1912.

On the surface, the "ten times fewer" locution seems to me to be a contradiction in terms. How can something less be 10 times fewer?

I can understand readily how, for example, 2012's bee population of, say, 90 million can be one-tenth (point one) less than 1912's population of 100 million, but ten times fewer?

I'm confused. Which expression is "more" correct?

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    "Ten times fewer" can be confusing. "One tenth the number" is not confusing. So: choose which to use, depending on whether you want the result to be confusing or not. – GEdgar May 19 '13 at 19:19
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    In any event there is no way to be sure that the writer KNOWS the truth of any statement he makes. Not unless he knows and can document the NUMBERS ... be it bees, rainfall, population, whatever. If he cannot, he should not be trusted. But if he can, and does, any of us can see clearly how much bigger or smaller is any number he writes. So he should provide the numbers. In the business of writing to inform, he should give us information. And we should demand it. – user46541 Jun 23 '13 at 0:26
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    @rhetorician: You wrote "one-tenth fewer honeybees". I can make myself believe that you said "10% fewer honeybees". This is not at all like "one-tenth as many honeybees" which is what you meant to say. – Les Jul 24 '14 at 12:59
  • @Les: Frankly, I'm still a little confused, but isn't a "10 percent reduction" in the number of bees 10, if there are 100 bees to begin with? And one-tenth fewer bees, or 10, means there are 90 bees left (again, if the original number is 100). Aren't both statistics two ways of saying the same thing? Maybe you can un-confuse me? Don – rhetorician Jul 24 '14 at 16:19
  • one-tenth fewer would be 100 - (0.1 * 100) or 10 fewer or 90 total in your example. one-tenth as many would be 0.1 * 100 or 10 total. But then maybe I'm the one that's confused and my confusion only makes sense to me. – Les Jul 24 '14 at 20:30

"There are ten times fewer pollinating honeybees worldwide today..." IMO is definitely incorrect and meaningless. It implies there is a property called "fewness", that can be possessed in different amounts. In the same way, "ten times slower", "ten times cheaper", "ten times colder", "ten times closer".

"There are one-tenth fewer honeybees worldwide than there were in 1912" This is correct, but for a different statistic: one-tenth of the bees have disappeared, leaving nine-tenths behind.

"There are one-tenth as many pollinating honeybees..." is a correct way to express the statistic...

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    It is not meaningless. It is perfectly clear in meaning. – Colin Fine May 19 '13 at 18:32
  • @User58220: Your correction is correct. Thank you. I did go back and make a few corrections myself, particularly with the numbers I carelessly bandied about. I THINK I agree with Colin Fine that 10 times fewer is, perhaps, readily understandable. About the only way to prove him right (or wrong) is to give a random sample of people (not mathematicians) an actual question involving numbers and the locution "ten times fewer." I also agree, I think, with your statement about "a property called 'fewness,' that can be possessed in different degrees." I need to let that percolate a bit! – rhetorician May 19 '13 at 19:16
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    @ColinFine I would probably understand what “ten times fewer” meant ... while noting that it's awkward, and wondering why the writer didn't use “one tenth.” – Bradd Szonye May 19 '13 at 20:33

I would disagree with the previous answers and state that "ten times fewer" is not wrong but merely idiomatic. Yes, if you dissect the words it doesn't mean what it literally says. Yes, it can potentially be confusing, especially to non-native speakers. No, its meaning is not mathematically precise. All of those things can be said of many idioms. The fact remains that the phrase is in common usage, dating back centuries.

Saying "one tenth as many" is more technically accurate, and would be preferred if you were writing, say, an engineering specification. But in everyday usage, "ten times fewer" or "ten times slower" will get the job done.

This is apparently oft debated. See Language Log and The Volokh Conspiracy for some other slants on the debate.

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  • Plus one, and thank you for your contributions to the discussion. The hyperlinks you provided are spot on. Guess I used the completely wrong words in my online search! The Volokh Conspiracy article contains some heavy-duty reading (for me, that is), but I'll read it over a couple more times and parse it when I'm good and rested. – rhetorician May 20 '13 at 2:47

Times means (to) multiply (ODO & Collins), as in Have you learnt your 10 times table?

As an example, let's start with 500 items.

Then 10 times as many will give us ...
BUT, wait a minute, 10 times as many as what? 10 times what? Obviously (and implied) 10 times as many as we started with.
So, 10 times as many (as we started with) will give us 5,000 items.
10 times more (than we started with) (and read strictly) will give us 5,000 more items plus the original 500, will give us 5,500 items (though no doubt this expression is normally intended to mean the same as 10 times as many).

Now, 10 times fewer (or less) (than we started with) must mean 10 x 500 = 5,000 fewer than we started with, so we now have 500 - 5,000 = -4,500 items, so we now have a negative number of items.

If, instead of items, we were to refer to US Dollars (and use as much instead of as many, and less instead of fewer), then those calculations make perfect sense: you started with $500 credit and finish with $4,500 debit!

Yes, when talking about a reduction 10 times is probably intended to mean one-tenth - but it doesn't: that is not what the words mean.
And, as User58220 pointed out, 10 times fewer is doubly wrong if it is intended to mean one-tenth as many because, even if you read it as one-tenth instead of 10 times, one-tenth fewer still leaves you with 90% of the starting number.

So, in answer to the question, I would say that almost all instances of expressions such as X times fewer/less/slower/cheaper/etc. are wrong, and, even though the general intent may be clear, they can also be ambiguous, e.g. one-tenth less or one-tenth as much.

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  • Plus one, and thank you for your contribution to the discussion. – rhetorician May 20 '13 at 2:29
  • And we haven't even started on "We're past the highway accident, and going half as slowly as we were..." – DJohnM May 20 '13 at 5:16
  • "What the words mean" is what the speaker intended them to mean and/or what the hearer understands them to mean. A mathematical analysis is irrelevant to the meaning. Now if, as you've said in a comment, the intended meaning is not clear to you, that's unfortunate and we have a case of ambiguity (horror!). But I suspect that in fact the intended meaning was perfectly clear to you, and your insistence on finding a different meaning is a perverse subversion of the process of communication. – Colin Fine May 21 '13 at 16:19
  • @ColinFine (1) The OP stated There is something about that wording that bothers me, and I'm not sure why. ... I'm confused. Which expression is "more" correct?" My answer was attempting to address those questions - analysing *why the wording might bother him and which expression might be considered more correct. – TrevorD May 21 '13 at 23:35
  • @ColinFine (re:(1) above - sorry italics wrong in above answer - can no longer correct them.) (2) As regards your suggestion that the words mean what the speaker intended them to mean, I can't agree. Suppose a speaker unintentionally says go west when he meant go east, then, on the basis of your argument, west means east because that it what the speaker intended. – TrevorD May 21 '13 at 23:44

I'll weigh in on this one simply to add information about the reality in biomedical journals.

The incidence of thyroid cancer was ten times lower/less in group A than in group B.

is common. It's idiomatic. It's illogical. But that's the way people write it, both native Anglophones and non-natives.

I'll paraphrase Colin Fine's comment:

Language usage has little to do with logic. Idioms are grammar-proof and are just the way people use the language.

Bill Walsh, former editor of the Washington Post, lamented this usage in The Elephants of Style (p. 121): "Even worse is times less. One time less equals zero, so how can a currency be worth five times less than it used to be worth? Multiplication comparisons are not reversible: If the former value is five times the current value, the currency is worth one-fifth as much, or 80 percent less." This is a logical analysis, but writers don't listen to the logic: they imitate the other writers in their field, just as Gustave Le Bon said in The Crowd (1895). If everybody else does it, it must be the thing to do, so throw away your brain and follow the crowd.

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    Thank you for weighing in! Your cite to "The Crowd" immediately brought to my mind Moses' words to Israel: "You shall not follow the masses in doing evil, nor shall you testify in a dispute so as to turn aside after a multitude in order to pervert justice" (Ex 23:2). Of course, following the masses in using illogical idioms is not tantamount to doing evil; far from it! Nevertheless, you make a good point. So often in language usage it's "Monkey see; monkey do," and who among us is not guilty of such imitation? To paraphrase Jesus, "Let him who is without idioms cast the first stone"! – rhetorician May 20 '13 at 14:06
  • No, almost always in language it's "monkey see, monkey do". That's how language works. – Colin Fine May 21 '13 at 16:15
  • @Colin: For linguistic monkeys, yes, that's how it always works. They never think about what they say or how they say it. For those of us a little higher in the evolutionary tree, however, it's more like, "monkey see, monkey think about it, monkey do what's best in context". You've been reading too much Pullum: he's a hypocrite, by the way, as are all dogmats who make incredible claims about about the world. – user21497 May 21 '13 at 21:32
  • @ColinFine: I agree with you, up to a point. Yes, even "creative writing" is to some extent (a large extent?) derivative and perhaps even imitative. Occasionally, however, using the same basic tools that are available to all of us who are literate, a Hemingway, or a Dickens, or a Shakespeare, or a Harper Lee comes along, and with a unique amalgam of yeoman skills; self-discipline; and powers of invention, organization, and style, they contribute something to human culture that is sui generis and at the same time incapable of being imitated in "monkey see, monkey do" fashion. – rhetorician May 22 '13 at 4:38

Language has very little to do with logic.

If the meaning is clear - and I think it is, here - what else matters?

I don't think I'd say ten times fewer, but I understand what people mean by it, and (I think) why they say it that way: they're used to expressing quantities by multiples ten times bigger, ten times as quickly. Would you have the same objection to ten times slower?

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  • Not many people use the expression - but then fewer use 'ten times as many' than the probably inaccurate 'ten times more'. books.google.com/ngrams/… – Edwin Ashworth May 19 '13 at 18:39
  • @Colin Fine: Yes, I would still object! I think User58220 is on the right track--if not at the destination itself! – rhetorician May 19 '13 at 20:28
  • @Colin Fine: "Language has very little to do with logic"? Oh contraire, mon frère! While language can be quite illogical, with all those "exceptions" to the rules (in grammar, punctuation, spelling, verb tenses, and more), logic could not exist without language. If there is no language, there is no thought. If there is no thought, there is no logic. Where do these statements place me within the plethora of schools of philosophy? I haven't a clue, but I'm pretty sure those statements contain at least some validity, if not veracity. – rhetorician May 19 '13 at 20:40
  • @Colin But the meaning often is not clear (see User58220's & my answers). So, would you use "If the meaning is clear ... what else matters?" as a response to any question of grammar, etc. where the meaning was otherwise (apparently) clear? If so, why do we discuss the meanings and intent of constructions? Let's just let everyone use their own version of grammar. But also, as clear from many questions here, non-native English speakers often misunderstand meanings that may be clear to native speakers. By using incorrect expressions, we're probably only confusing them further! – TrevorD May 20 '13 at 0:11
  • @rhetorician: so language has to do with logic at least this far, that you can express logic in language. I will happily grant that; and observe that language has just as much to do with galaxies, gaussian distributions and peculiar shades of green. – Colin Fine May 21 '13 at 16:13

Think of it as a rate. If a person ran a race 10 times faster than last time, he took 1/10th of the amount of time to run that distance. If he's 10 times slower, he covers 1/10th of the distance in the same amount of time. Rephrasing the rate change in either distance units or time units is acceptable.

For the honeybees, let's make it a rate of 100 bees per farm. If the rate was fewer, let's say 100 bees per 10 farms, then it's 10 times "fewer". In other words, 1/10th of the bees remain.

It's still confusing, but I hope this helps after as many years it's been for this question.

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