6

When comparing two quantities, say $x_1, x_2$ or something casually, I frequently use the phrase "they're within X%" but I use it rather loosely because mathematically, to compute the percentage difference it depends on whether you use $x_1, x_2$ as the reference.

e.g., suppose $x_1=90, x_2=100$, the absolute percentage difference is either $$ \frac{10}{100} $$ or $$ \frac{10}{90} $$

If I was asked "check if $x_1, x_2$ are within $10\%$", is there some idiomatic interpretation for this? I think I would naturally want to choose the interpretation with the larger denominator (hence smaller percent differential).

roulette01
  • 403
  • If someone asks you an ambiguous question, then you should ask the asker to alleviate the ambiguity. – Blue Feb 02 '24 at 05:14
  • @m-stgt I edited the "absolute" into the OP, but I think usually when we talk about percentages we think in absolute terms – roulette01 Feb 02 '24 at 05:18

1 Answers1

3

It depends upon the direction of change. For example, suppose a stock price goes from $\$90$ to $\$100$. Then the change is $\frac{10}{90}\approx 11\%$.

If the stock price goes from $\$100$ to $\$90$ then the change is $-\frac{10}{100}=-10\%$.

In the first case we would say that the stock price increased by approximately $11\%$ and in the second, we would say the stock price decreased by $10\%$.

To say that the difference between two numbers is a certain percentage doesn't really make sense. We start from a quantity and measure its change.

John Douma
  • 11,426
  • 2
  • 23
  • 24