This may be more of a semantics issue than a math question, but I want to make sure.
How does one calculate the percentage difference between two numbers? I looked at a few math websites and I get different answers. Some calculate the percentage increase, and others the percentage decrease.
If I was given a task to calculate the percentage difference between sets of two numbers, how would I go about giving the corrects figures?
For example, if my first numbers were comparing 5 and 10, there is a 100% increase from 5 to 10, but a 50% decrease from 10 to 5.
Is there a commonly accepted way to compare the difference in % between two numbers that doesn’t involve knowing if there was an increase or decrease?
That’s just the nature of the beast. It comes up in retail with margins and markup. If a product retails for $10 and costs $5 wholesale it sells at a 50% margin and is a 100% markup.
Just make sure that you use the write words to describe the numbers. For example, if gas is $2.50 now and was $2.00 last year you can say either gas was 20% cheaper last year or the gas price increased 25% this year over last.
You have to establish the baseline, as it were, to which you will be comparing other things - otherwise comparison isn’t really meaningful. The moment you’ve done that, it becomes simple: either the first number is 100% more than the second (in which case the second number is the baseline) or the second number is 50% less than the first (in which case the baseline is the first number).
It all depends on how to want to present your data, and I’m not aware of any established way of doing it.
It’s not a question of increase or decrease, it’s a question of which number you’re taking the percentage of. Asking the percentage difference between 5 and 10 is meaningless. You have ask the percentage difference of what.
The difference between 5 and 10 is 5, right?
5 against a base of 5 is 100%, so from 5 to 10 is a 100% change. It also happens to be an increase.
5 against a base of 10 is 50%, so from 10 to 5 is a 50% change. It also happens to be a decrease.
Let me ask the question of the OP in a simpler way. Is 5 less than 10, or is 10 greater than 5?
Answer: both are true, it’s not either/or. But of the two ways of saying it, one makes more sense in the larger context of why you’re comparing them in the first place.
Once you know why, you’ll know which comparison to make & hence which percentage to calculate.
Always compare to the initial value or the true value (if you are doing an experiment). Never compare to the final value or the number you obtained as a result of experimentation.
If the price went up from $2.00 to $2.50, the percent difference would be 0.50/2.00.
And if you derive these numbers as part of your job the correct answer is which ever makes your boss look better. So in the same report you can say “sales are currently 20% higher than last year’s volumes” (dividing difference by past figure) and “bad debts were 33% higher last year” (dividing difference by present figure).
The problem noted in the OP can be avoided by using logarithmic scales for ratiometric comparisons.
The ratio between 5 Watts and 10 Watts is 3dB, or -3dB if you view it the other way. The sign tells you if there was an increase or decrease, and the number tells you the ratio between the two.
