"Ten times fewer the number" versus "one-tenth the number"

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?

Solution 1:

"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...

Solution 2:

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.

Solution 3:

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.