To keep it simple with the numbers, let’s say…

Sales in 2012: \$100
Sales in 2013: \$250

This is a math and language issue that I am fuzzy on. What are the most impressive (albeit not misleading) ways of describing the change in sales:
“Sales increased 150%.” —> 150/100

“Sales in 2013 were up 250% over 2012.” ----> 250/100

Are both of these correct? Suggestions for other wording?

The second one looks wrong to me… if sales were only up 100%, then they would have made \$200 that year. Making \$250 means that sales were up 150%.

the percentage increase is 150%. you can’t change that.

you could say sales in 2013 is 250% of what we did the year before. while true this might be misleading, as people usually state percentage increases. or you could skip percentages altogether and just say that compared to the previous year, sales more than doubled in 2013; or we almost tripled our sales in 2013.

The second one is wrong. This is not a matter of opinion.

100 -> 101 = 1% increase
100 -> 110 = 10% increase
100 -> 200 = 100% increase
100 -> 250 = 150% increase

100 -> 250 = second year’s sales were 250% of the first year (NOT a 250% increase)

Typo in my 2nd example but, in any case, agree that the 150% figure is the way to go.

Thanks, everyone!!

what is the typo?

Even Scientific American (!) recently blundered, by talking about a carbon fiber that was “One hundred times as narrow as a human hair.”

I don’t see that as indicating addition. I see it as indicating multiplication, as opposed to division. “Two-and-a-half times less” would mean to take the original and divide by 2.5 (aka 40% or, in advertizing speak, 60% off).

Saying “two and a half times less” is really really horrible and imprecise - it is much better to just say 60% discount,

or if you like use something like “1/4 the price”

There is no such thing as two times less

But you could say “our total sales were two and a half times what they were in the previous year”, which would be accurate and not misleading. Just depends on how you want to present it. I agree with everyone else that with percentages, you either have to say “a 150% increase” or (less good than any of the above) “sales were 250% of the sales the year before”.

I’d suggest not saying anything about the percentage increase, just to avoid confusion. Instead, you might say, “Sales increased from \$100 in 2012 to \$250 in 2013.”