How to find which percentile out of 100 a negative number is?

Question

I'm having some logic/math problems in a program I'm trying to fix. So, suppose I have three values, 30, 25 and -15. The sum of these values is always going to be 100%. But I also need to know which percentile out of 100 the -15 is, if there is any, since the negative numbers need to be counted in the total sum. If I count the sum as 40, as in adding 25 and (-15), it's easy, but I wouldn't be able to know which percentile was the -15 because it is now a +10. I've used this formula: P% * X = Y where P is what % of X is Y but for it I would have to count 40 as being total, but I don't think I can just sum the numbers up. Does this make any sense? I'm sorry for not being able to be clear enough.

Answer 1

The only (somewhat) sensible calculation I can give you is the following: just follow the same rules that you follow when all the numbers are positive:

• Add them all together ($30+25-15=40$)
• Divide each of them by the total sum and multiply by $100\%$: $\frac{30}{40}\times 100\%=75\%, \frac{25}{40}\times 100\%=62.5\%, -\frac{15}{40}\times 100\%=-37.5\%$.

As you see, some percentages will end up being negative. In this case, you end up with the following percentages: $75\%, 62.5\%, -37.5\%$ which do add up to $100\%$.

It is the whole other question whether this calculation gives you what you need. (I cannot tell from your question alone.)

Also note, if your numbers add up to $0$, this calculation does not make sense.

Answer 2

"Percentile" does not mean

• "percentage ratio of the sample value to mean"
• "percentage ratio of the sample value to the sum."

It means

• "percentage fraction of samples less than the given sample" or
• "percentage fraction of samples less than or equal to the given sample" or
• rounded or interpolated variations thereof, dependent on who you ask.

For your samples, the percentile of each sample depends on the definition, but

• for $-15$ is $0$ at least, $34$ at most;
• for $25$ is $33$ at least, $67$ at most; and
• for $30$ is $66$ at least, $100$ at most.