When we talk about percentiles, if the lowest number in a set of 100 is the 0th percentile then that should make the highest number 100th percentile according to my understanding. But one of the questions (PFA) explains that the highest number is the 99th percentile and not the hundredth which makes the second largest 98th, third largest 97th and so on and so forth. If the provided explanation is correct, should I just memorize this as fact or is there a proper rationale to it that I can look up somewhere?
There are two definitions of a kth percentile
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k% of the data are at or below a certain data point
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k% of the data are strictly below a certain data point
If i recall correctly, GRE uses definition 2). In light of this, something like the 100th percentile is not possible because that would imply that a data point (let’s say a score) is greater than all the scores in the data set (even greater than itself).
However, do note that a 100th percentile is possible according to definition 1) though. It all boils down to which definition you’re falling back on.
Similarly, definition 1 doesn’t allow for the 0th percentile like definition 2 does.
I think that clarifies most things for me, so I would like to thank you for that. Coming to what my malaise with the definitions are, it wouldn’t be wrong to state that mathematically both 0th and 100th percentile make sense and we’ve seen this irl in a lot of exam where the highest attained score gets the 100th percentile. The claim that (2) makes about 100th percentile only existing if the data point is larger than itself does not seem coherent enough to be an axiom. A similar contradiction is faced in (1) as the lowest score should de facto be the 0th percentile as there’s nothing smaller than that data point, even if it is equal to itself. Would it just be the productive move to accept (2) in a dogmatic way and move on?
I doubt the GRE would ask you questions that hinge specifically on which definition you use.
Also, I wouldn’t really call those definitions “axioms”. 100th percentile and 0th percentile both make sense if u choose the appropriate definition tbh. It can’t both make sense on one definitions cuz there would be more than 100 partitions, which contradicts the notion of percentiles.
As for your final qualm, i believe you should be fine as long as you’re cognizant of at least one of those definitions. If you want to be extra safe then you can stick to definition 2).
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Sweet, thank you again. I’m personally also not sold that ETS would test the type of thinking Greg’s questions make us do but I’ll be sticking to (2) for the off-chance that they suddenly decide to.