Reduced by a factor of 2500%?

[blue2020]

"The number was reduced by a factor of 2500%".

Does that makes sense? I thought it should be "it was reduced by a factor of x" or "it was reduced by x%". Not a mix.

Thank you.

 

[Dr.Peterson]

I certainly don't like it; but let's see if we can make sense of it.

"Reduced by a factor of 3" would mean divided by 3.

"2500%" means 2500/100 = 25.

So the phrase "reduced by a factor of 2500%" means "reduced by a factor of 25", which in turn means "divided by 25".

For example, if a population was 100,000 people, and it was reduced by a factor of 2500%, that would mean it changed to 4000.

So it does make sense; but how many people would know what it means? And might the author have meant something else? I have no idea. Would they think that "reduced by a factor of 100%" meant anything?

 

[blue2020]

The author meant "reduced by a factor of 25" - 500,000 to 20,000. I think he is trying to make it sound worse by using 2,500%.

So it is mathematically correct to use percentage?

Thank you!

 

[Dr.Peterson]

That's my opinion -- it's mathematically valid but misleading, so I wouldn't do it. And, again, it's possible the author didn't mean what they wrote.

On the other hand, yesterday in a quack medical ad I saw a claim to reduce something or other by 400%. That is mathematical nonsense! (Well, unless that quantity could be negative, which it couldn't.)

 

[blue2020]

Thanks again, I appreciate it.