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    $\begingroup$ If you regard the maximum as the 4th quartile then I'd suggest counting must start with regarding the minimum as the 0th quartile. $\endgroup$
    – Nick Cox
    Commented Jun 13, 2015 at 11:52
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    $\begingroup$ Can percentiles also be scaled to be between 0 and 1? Ex: does it make sense to say percentile(array, 0.5) (the median)? $\endgroup$
    – Cam.Davidson.Pilon
    Commented Jun 23, 2015 at 0:50
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    $\begingroup$ The "percent" part of "percentile" comes from "cent" for 100. If you scale between 0 and 1 you have proportion. Of course, they are equivalent. $\endgroup$
    – Peter Flom
    Commented Jun 23, 2015 at 11:12
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    $\begingroup$ You can make 1000-tiles or 10,000 tiles or whatever you like. $\endgroup$
    – Peter Flom
    Commented Apr 22, 2016 at 11:09
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    $\begingroup$ @JosephGarvin the point Peter Flom is trying to make here is that quantiles are technically infinitely divisible whereas quartiles are not. E.g. you can have a 11.5625th quantile but only a 1st or 2nd quartile. $\endgroup$
    – gosuto
    Commented May 5, 2020 at 21:12