# What does "25% less than X" mean ?

The media constantly says that X is 30 times less than last last year, or 11 times less than Monday. What does that mean ? How does it translate into reality? How is one to calculate such a figure?

Why don’t they say 25% less or any percentage if that is what they mean?

I have seen academics use this phrase and I have written to some and asked many people who should know and I have never received an answer.

Could it come from some discipline like Chemistry or physics, or some other culture?

So your question is really about what “X times less” than something means, as opposed to “25% less than X,” which is pretty straightforward (total is X-0.25x). “Times less than,” to me, is meaningless.

“Y is 25% less than X” means Y = (1-0.25) * X

“Y is 25% more than X” means Y = (1 + 0.25) * X

“Y is 11 times more than X” means Y = 11 * X

“Y is 11 times less than X” means Y = X / 11

It is sort of an idiom, but in my field (computational physics) I’d know exactly what was meant by “11 times less than X”.

Where it really gets confusing is in statements like “The rate of asthma in the US increased by 3% last year, to 16.3%”.

What was the rate in the previous year, 13.3% or 15.8%?

I’d say 15.8%. If it changed from 13.3% to 16.3%, you’d say “increased by 3 percentage points”.

Assuming X is 9900

30 times less than X is 330
11 times less than X is 900
25% less than X is 7425

It’s the opposite of “times more than”.

A hundred is five times more than twenty. So twenty is five times less than a hundred.

Except mainstream media is frequently careless about making that distinction, especially in headlines or teasers (i.e. “after the [commercial] break …”).

I guess that makes some sort of sense to me. I’ve always wondered what in the f* this construction meant, as these sorts of things are not reciprocal. Like 40 is 100% more than 20, but 20 is 50% of 40 (and this distinction is screwed up enough in reporting when talking about percentage increases and decreases that I disregard the reporting and just look at the starting and ending numbers. ETA: And then you have the whole percent vs percentage points distinction mentioned above. All of this drives me nuts.)

Many interesting responses, but the usual expression is "the flu rate this year is 18 times less than last year… 200 pound lesbian dwarfs who rode tan horses more than twice a week for 89 years after dusk were 84 times less likely to contract cancer of the left side eyebrow…meanwhile in Australia, the year the rate of men preferring sheep to roos was 11 times less than in 1492…

There seems to be a mysterious essential figure missing in the construction(s).

“X times less than Y” always means Y/X. One can argue about whether the phrase should be meaningful at all, but it’s not ambiguous: It’s never used to mean anything other than that.

The bit about percentages vs. percentage points, though, is commonly-enough confused that if you ever see either, you should double-check what what was actually meant.

Slashdot the other day had this in an article blurb the other day:

The actual article it leads to doesn’t contain the bad Math. It was done by the submitter and the admin who posted it didn’t catch it. For some reason, Slashdot rarely fixes such glaring errors.

So, what were the correct numbers? At most two of those three are right, but I can’t come up with any pair of two correct numbers that would leave room for any plausible math error that would give the third number.

The most probable math error with just one incorrect number that I would postulate would be that the business started with 160 employees, the 25% and 40 are correct, but the headline writer incorrectly subtracted the 40 twice to generate the incorrect 80 number.

Or they had the 120 final number from sources, but then confused it as being the initial number and did the math again subtracting 40 to get the 80 number.

The article it linked to has:

No mention of 120 (or 160) at all. Methinks the submitter remembered 120 from another article and confused before/after numbers. The actual numbers don’t really matter. I was just pointing out how common this mistake is, even on a well moderated site like Slashdot run by very tech-ish type people who should be able to parse such statements quickly and spot the error. (I noticed it immediately.)

Also if something has increased by ‘a factor of x’ that means it has increased by more than 100%. A factor of 2x or 3x would be 200%, 300% etc. and a lot of average people are totally confused when you say anything is over 100%…

Something can be 25 % less this year than last. But something that is 25 times less means nothing or you can guess.

If something is “25 times less” than last year, then it’s 1/25 of last year (e.g. 100 last year, 4 this year). Not ambiguous at all.

No that is division normally referred as being 1/25 of last year.

25 times means multiply first then subtract.

Trouble is that ‘five times more’ already contains an ambiguity.

A hundred is five times twenty (the ‘more’ clause is not necessary)

‘five times more than twenty’ could mean 100, or it could legitimately mean 120 ([five times twenty] more [than twenty])

Either way, both interpretations involve factors, but in the case of ‘five times less’, the factor is unknown.

I concede that when people say ‘five times less’, they probably mean ‘one fifth of’, and the construction may be widespread enough to be currency, but it doesn’t make logical sense.