A percentile is just the percentage of things that fall below or equal a certain value.
For example, if a person were the 69th smartest person in a room of 100 people, they would fall into the 32nd percentile because they are smarter than 31 other people (plus the original person 32/100 is 32%). They would also fall into the 50th percentile because 32 is within 50. That person would fall into any percentile that doesnt exceed 69.
You can also do this in the reverse in the case which you did in the first example you used. Saying someone is in the top 30th percentile for the intelligence example I used would mean that they are within the 30 smartest people in the room.
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