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    $\begingroup$ Useful, but a very slight awkwardness in the middle. There is no implication in the definition that any discrete set of quantiles you focus on must be selected as regularly spaced in probability. For example, looking at something like 1, 5, 10, 25(25)75, 90, 95, 99 % points is a common part of variable summary. $\endgroup$
    – Nick Cox
    Commented Jun 14, 2015 at 13:33
  • $\begingroup$ @NickCox My definition for quantile was to use the definition from Wikipedia en.wikipedia.org/wiki/Quantile "Quantiles are values taken at regular intervals from the inverse of the cumulative distribution function (CDF) of a random variable." $\endgroup$
    – I Like to Code
    Commented Jun 15, 2015 at 14:14
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    $\begingroup$ Thanks for the reference, but I contend that using regular intervals is not part of any definition. Quantiles would not cease to be quantiles if you chose (say) 50, 75, 90, 95, 99% points. $\endgroup$
    – Nick Cox
    Commented Jun 15, 2015 at 14:49
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    $\begingroup$ I use Wikipedia every day fondly and distrust it mightily on anything like this. $\endgroup$
    – Nick Cox
    Commented Jun 15, 2015 at 18:26
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    $\begingroup$ If a specify an arbitrary value p in the interval [0 1] in the definition of Q(p) above and want to find the corresponding x, would x be called the p-quantile? $\endgroup$
    – Kavka
    Commented Aug 31, 2021 at 18:13