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Officially, there are three quartiles: They are the boundaries that divide any distribution into four equally populated intervals.

Confusingly, people also refer to these 4 intervals as quartiles!

Now, my question is if there is a usable term to easily and shortly refer to these intervals, and so that everybody will understand?

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    $\begingroup$ You’re looking for a name for the fraction of data? You can call it by that fraction. The lowest quarter; the third quarter. The Wikipedia article TMat linked agrees with calling these quarters. $\endgroup$
    – Arya McCarthy
    Jun 11, 2021 at 14:14
  • $\begingroup$ Can you provide a sample sentence with a blank where you would like to use this term? $\endgroup$
    – Matt F.
    Jun 16, 2021 at 15:08

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interquartile range, inderdecile range or more generally interquantile range can be used.

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    $\begingroup$ IQR is the difference between the third and first quartiles; IDR is between the ninth and first deciles. This is stated in the articles you linked. It’s not a name for the interval of data itself. $\endgroup$
    – Arya McCarthy
    Jun 11, 2021 at 14:13
  • $\begingroup$ Note the OP is interested in the interval between two adjacent quantiles. $\endgroup$
    – Richard Hardy
    Jun 11, 2021 at 14:16
  • $\begingroup$ Yes, exactly @RichardHardy Let's say I computed the three quartiles for my distribution, and do subsequent analyses on the four stratified intervals. What would be an easy, elegant, and correct way to label these 4 intervals? $\endgroup$
    – mjbeyeler
    Jun 11, 2021 at 16:38
  • $\begingroup$ In case there is no good word for these bins, I'm inclined to call the intervals "quartiles" and the official quartiles "quartile boundaries". Seems easy and elegant, but not sure if math folks would be happy about that. $\endgroup$
    – mjbeyeler
    Jun 11, 2021 at 16:49
  • $\begingroup$ @MichaelBeyeler, I think I understand your question but I do not have an answer for it. $\endgroup$
    – Richard Hardy
    Jun 11, 2021 at 17:12

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