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    $\begingroup$ A deeper question is whether quantiles etc. are intervals or points. $\endgroup$
    – Henry
    Commented Jun 13, 2015 at 14:20
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    $\begingroup$ The quantiles are defined as points. There is often ambiguity as between intervals and points for quartiles etc.; it does not bite very hard in practice, as context usually makes clear what is intended. I prefer the first quarter (rather than quartile), for the lowest 25%, etc. although it's too much to hope that the distinction will be universally self-evident without explanation. $\endgroup$
    – Nick Cox
    Commented Jun 13, 2015 at 17:22
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    $\begingroup$ My answer at stats.stackexchange.com/questions/235330/… has a fuller list of *ile terms, including dates of first use. Naturally additions and earlier sightings (citings!) are welcome. $\endgroup$
    – Nick Cox
    Commented Jan 16, 2019 at 16:43
  • $\begingroup$ Quartile relates to quarters, i.e. out of 4. Pencentile relates to percentages, i.e. out of 100. Quantile ... is just there to confuse you (it relates to quantity). $\endgroup$
    – Bernhard Barker
    Commented Nov 15, 2020 at 6:19