How do you calculate percentile?

Say I have the following numbers:

10
10
9
5
4
4
4
1


How do i go about calculating the percentile for each score? Is there a standard formula for figuring this out?

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You may want to explain what exactly you mean by "precentile" as there are some possible meanings. – Gadi A Nov 7 '10 at 22:52

2 Answers

Well, if they come sorted like that, you can:

1. Calculate the length of the list (in this case, 8)
2. Start going up in ascending order (from 1, for example)
3. Once you hit a number bigger than the number you want, count how many numbers are before it (if you're looking for 5, that would be 5 numbers because you stopped at 9)
4. Divide what you found in #3 by the length of the list in #1, multiply it by 100, and there's your percentile.

Otherwise, just count how many numbers are <= the number you're looking for, then divide it by the total. The above is just faster for when they come sorted.

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The $x$th percentile is the point where $x$ percent of the data lies below. Here you have 8 data points; $1$ is in the bottom $12.5\%$, so it is the 12.5-percentile. $4$ is the (top of the) bottom $50\%$ so it corresponds to the 50 percentile. $5$ is at the top of the bottom $62.5\%$, so it corresponds to the 62.5 percentile. Etc.

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