Is percentage ambiguous?
I hear statistics such as “this provides a 200 percent increase over the current gas mileage.” If your gas mileage was 10mpg before the increase, is the improved mileage 20mpg? or 30mpg? 20mpg is 200% of the original mileage, but 30mpg is a 200 percent INCREASE (20mpg) over the original mileage (10mpg) for a total of 30mpg. I’m good with math but I have always found this type of statement confusing. Is it just me? If your heart beats 100 beats per minute and changes to 110, would you call that a 10% increase? a 110% increase? An increase to 110%? Any and all of these?
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9 Answers
Your heart example is a 10% increase.
If you get 10 mpg, and then it improves to 20 mpg, that is a 100% increase.
Oh, I thought I would give you a simple calculation for percent increase. You take the new number divide by the old one and subtract one.
So, for instance, sales were 20 last year, this year they are 30.
30/20=1.5
1.5–1=.5 turned in a percentage is 50%, 50 percent increase.
Your heart example:
110/100=1.1
1.1–1=.1 or 10%
Does that help?
What @JLeslie says is true. But, people don’t always use the phrase correctly :)
“percentage” is not ambiguous; ignorant usage is. Math illiteracy (innumerancy) is using mathematical statements in an incorrect manner.
One of my pet peeves is “400 per cent reduction” – that means absolutely nothing!
That’s a good example @zenvelo. One interpretation is that we go from $100 bank balance to -$300. That’s subtracting 400% of the original $100 from the balance, but that’s never the number that the speaker indicates.
ahhhh math so exact and not open to interpretation. Isn’t it great that math is the only language spoken by the entire world.
@GeorgeGee I think you are still a little confused. Understandable, it can be tricky.
Let’s say you have $100 today and $200 tomorrow. That is a 100% increase.
By contrast, if you have $200 today and $100 tomorrow, that is a 50% decrease. A 100% decrease would mean you have zero, because 100% is the total amount.
In your gas mileage example: 200% of 10=20, so a 200% increase would be 10+20=30.
I agree with your conclusion for that example.
If you are talking about the increase then it has to be the difference in values that is 200% of the original, which would mean that the increase is 200% so the total is 30 mpg. If you want to talk about a change from 10 mpg to 20 mpg then leave out the word “difference” and just say that the mileage is 200% of its original value.
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