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It is my understanding that quartiles are the three points in a ranked data set which divide the data into four equal groups.

What are the groups called? How would I say a number belonging to the ranked data set belongs to a certain group? What are the various names given to the groups?

I also understand that quartiles might mean something else when applied to different fields, where they might use it not as the points but the range of data.

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  • $\begingroup$ Terciles are used to describe 3 groups, quintiles for 5, deciles for 10, ventiles for 20. What's wrong with using quartiles for 4 groups? In terms of the information between the intervals, are you referring to quantiles? $\endgroup$ – Mike Hunter Oct 26 '15 at 20:15
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    $\begingroup$ I've seen instantly forgettable distinctions between tertile and tercile. I am the last person to sneer at Latin, which was a major part of my education and much enjoyed, but I think that it's unrealistic to expect people to know so many terms, or to expect that people will look them up. It's much simpler to introduce the term quantile as soon as possible in people's education. $\endgroup$ – Nick Cox Oct 26 '15 at 20:28
  • $\begingroup$ The longest list of quantile terms I know is elsewhere on CV: stats.stackexchange.com/questions/235330/… I would be delighted to learn of (a) a more complete list or (b) additions to the list. To modify an old joke, minutiae are just minutiae, but the cataloguing of minutiae is real scholarship. $\endgroup$ – Nick Cox Oct 10 '20 at 9:19
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I don't think there is a universally accepted answer.

Some people are happy also to call the groups quartiles; and are thus explicitly or implicitly optimistic that any ambiguity will not bite, or at least can be clarified quickly in context, e.g. by inspection of some suitable table, graph and/or algebraic definition. There is a long history of such usages, sometimes distinguished by nuance, e.g. that the quartiles (values) may be called the lower quartile, median and upper quartile, while the quartiles (bins) may be called the first, second, third and fourth quartiles. (Such practice reminds me of those who want means to be population quantities and averages to be sample quantities, which to me has never seemed very convincing, not least because I really want the freedom to refer to sample means.)

Others would regard quarters as an alternative term.

The verbal alternatives all appear to buy greater precision by being more long-winded (and to some tastes more pedantic), say quartile-based bins, classes, groups or intervals.

In many ways the best solution is to avoid special words altogether: to be simply quantitative and talk about the first or lowest 25%, second 25%, and so on. [Grateful nod to @Glen_b for reminding me of this common practice.]

Yet another alternative is to avoid any such terminology altogether, but this is not always possible. There isn't a universal notation for quantiles either: for example, there are many idiosyncratic notations for median, but none seems even common.

The same terminological problem arises with any quantiles.

EDIT 8 Oct 2020 In almost five years since this answer I've seen the bins, classes or intervals delimited by quartiles (quantiles generally) often called by the same names. The ambiguity between intervals and the levels that delimit them is unfortunate, but seemingly here to stay. In practice the ambiguity does not bite hard. The natural selection at work is that longer-winded terminology such as quartile-based bins evidently seems too fussy to find favour.

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    $\begingroup$ An excellent answer. I find it amazing, and somewhat amusing that we really don't have one widely accepted non-ambiguous term for it, but we don't. [I am not even consistent within myself -- I would lean toward calling them "quarters", (usually adding "of the data"), but given its lack of wide use I'm as likely to say something else, like "lowest 25%" for example, or some longer phrase like "below the lower quartile", "between the median and upper quartile".] $\endgroup$ – Glen_b Oct 26 '15 at 21:04
  • $\begingroup$ @Glen_b Thanks, especially for the reminder about lowest 25% etc, which certainly deserves mention in any complete answer, as now edited. $\endgroup$ – Nick Cox Oct 26 '15 at 22:00
  • $\begingroup$ Also bucket. Again, it can refer to either the subinterval (i.e. max and min values), or the set of values falling in that subinterval. $\endgroup$ – smci Oct 27 '15 at 0:21
  • $\begingroup$ Thanks for the answer Nick Cox (+1) and @Glen_b for the additional info. I'm surprised there is no conventional term for the groups. It seems like an obvious thing to use once the quarters have been created and to talk about it with others. I will mark it as the answer in a couple days to see if there's any other responses. $\endgroup$ – ilovefigs Oct 27 '15 at 1:01
  • $\begingroup$ Would it be considered wrong to use quartiles that way, where one would want to discuss which group one of the numbers belong to? $\endgroup$ – ilovefigs Oct 27 '15 at 1:10

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