# English adjective derived from Latin for “per equal amount of datapoints”

I'm not completely sure if this is the correct place to ask this, but let's try. Many thanks in advance.

I would like to invent a term for an average per equal amount of (sorted) data. With that I mean the average for the first N number of measurements, and then the average of the next N measurements, and so on. If it's not entirely clear what I mean by this, that's not such a problem.

So I'm looking for an adjective to specify the average that is derived from Latin. Something analogous to equidistant or equipotential. But with the part after "equi-" refering to the amount or number (in "equal amount of data/number of datapoints"). Does something like that exist?

Alternatively, if it doesn't, I would like to invent something. But not being a Latin expert, I don't really know which Latin word would fit best, and I'm not sure if I combine them correctly.

• "copia". This could then become "equicopian"? Or …?
• "quantitas". I don't really know how this would be used.
• "continent". As in containing, cfr. "equidistant". This would become "equicontinent".

Any suggestions?

Perhaps greek might be better, using "iso-"? Perhaps

• "mer" . This would become "isonomerous". This exists in biology, so it might be confusing.
• "posotis". Would become "isoposotic"

EDIT: To be more precise, I should say that my data consists of a variable y which is dependent on a variable x. I want to order my data according to x, and then take the average (as explained above) of y.

• what about equinumerous? I also thought of batch average: it is neither Latin, nor necessarily constant in number, but at least in simulation is used exactly in the sense you explain – Rafael Jan 25 '17 at 19:22
• Can you clarify how this word would be used? I'm imagining something like the "The equicopian averages of X are 3, 4, and 3." – brianpck Jan 25 '17 at 19:31
• In similar cases, words like percentile and quartile, etc. are in common use. Would they fit your case? – Cerberus Jan 25 '17 at 19:58
• @Rafael Yes, that's what I thought. Good to know. Only thing is, the average is not really equinumerous, the sets over which the averages are taken are. – Lu Kas Jan 26 '17 at 12:45
• @Rafael I actually already did before i posted here, but with the idea of asking if there already existed a word. It seems like none exists, but a recent answer did also give a good suggestion for a new word. – Lu Kas Jan 26 '17 at 16:09

I'm not entirely sure if I understand your meaning, so please comment if this isn't what you're looking for.

But it sounds like you want a word meaning the average of each group of data, divided by quantiles of the domain?

I agree with Cerberus about using quant- as the root, meaning (roughly) "amount".

-il- is still the best I've come across for dividing into equal parts, giving quantil-.

In mathematics, the prefix co- is generally used for a counterpart to something else: domain and codomain, sine and cosine, kernel and cokernel. So co-quantil-

Then finally, something to turn it into a noun or an adjective. This is the tricky part. Plenty of these survived from Latin into English, but not all of them are useful for you:

• co-quantile
• co-quantility
• co-quantilian

And so on...

Out of all of these, co-quantilian sounds the most pleasing to me. It's not perfect: -ian is usually used on names, which this is not. But it sounds better as a de novo term than "co-quantility".

• Hmm, I like your approach. Quantile average, is the obvious and perfect word for the averages of the x variable. Then in analogy with domain and co-domain, co-quantile average (I would use a hyphen to make the word look less exotic) would be a logical counterpart for the averages of the corresponding y values (which is the one I'm looking for). I'm thinking about marking this as solution. I'll definitely upvote. – Lu Kas Jan 26 '17 at 16:06
• @LuKas Bear in mind that "quantile" implies (in my experience at least) that the division is based on and ordering. If the division of the data into the different bins is completely independent of the data values, I would be confused. I would expect both a "co(-)quantile average" and a "quantile average" to bin the data in a specific order. – Joonas Ilmavirta Jan 27 '17 at 4:52
• @JoonasIlmavirta Yes, that is also what I mean. I have data which consists of a variable x with a corresponding variable y. I want the averages of y of the sets of equal amount of data, but ordered according to x. So then co-quantile average seems good fitting. – Lu Kas Jan 27 '17 at 11:25
• I marked your answer as correct, but I would suggest adding the hyphen, because without it I find one interprets it as coquan-tility or so, if you understand what I mean. That is also why your answer didn't really appeal to me immediately. – Lu Kas Jan 27 '17 at 11:31
• @LuKas Then I agree that this is a good word. I didn't know any ordering was involved. – Joonas Ilmavirta Jan 27 '17 at 15:37

I would call it an isoplethic or homoplethic average measurement.

It is a Greek compound formed of ἴσος ("same", "equal") and πλῆθος (which usually mean "big quantity", but could be used more specifically with the meaning of "quantity", "amount").

Furthermore, the term "isoposotic" that you suggested is not attested as a compund in ancient Greek, while the adjective ἰσοπληθής is used in the same way you look at:

Thuc. 6,37,1: ὁπλίτας ἰσοπλήθεις τοῖς ἡμετέροις "hoplites in the same quantity as ours"

Xen. Cyr. 2,9,7: σχεδὸν δὲ καὶ οἱ ἱππεῖς ἦσαν ἑκατέρων ἰσοπληθεῖς "the knights of both sides were almost the same in number"

The term is also used by ancient mathematicians like Euclides and Pappus.

While "isopleth" already exists, I think that "isoplethic" shouldnt' create confusion (but you could mix up Latin and Greek and invent the term "equiplethic").

• Sounds good, but I'm a bit reluctant of using a term that already exists for something different(?). – Lu Kas Jan 26 '17 at 12:44
• ok, sorry, I guess I read/reacted a bit too fast. But so isopleth seems to refer to the same measurable quantity, which in this case would thus refer to the same values of x, rather than the amount of measurements ... Concerning the mixing of Latin and Greek, do people Latinists and Greekists(?) usually not laugh at that (though I don't know if that would matter). – Lu Kas Jan 26 '17 at 16:20

If I understand correctly, you want to divide your data into equally large sets and calculate an average for each set. Equally large sets are often called equinumerous. Finite sets with the same number of elements are equinumerous, but the concept becomes more complicated for infinite sets. All the definitions using bijections or cardinals or any other tool will have the correct intuitive meaning when applied to finite sets.

Alessio's suggestion of isoplethic or homoplethic is also good. It can be useful to use a new word if you want to define something that is not equivalent with a previously named and known concept. Giving a new name to an old thing is rarely a good idea.

I would suggest a different approach to naming the concept, though. You divide your data into equally large chunks. Such division can be called equipartition(ing). I would prefer to include this sense of dividing into equally large sets; speaking only of equally large (equinumerous, isoplethic, or whatever you want to call it) conveys the setting only partially. The prefix equi- is of Latin origin (aequi- in Latin) and the Latin verb partire means sharing.

You could say that equipartitioning a set means partitioning it into equinumerous subsets. In practical situations I believe equinumerous means "of almost the same size". You cannot equipartition a set of million datapoints into 17 subsets, but the difference between 58823 and 58824 points is hardly going to be of practical relevance.

I would say that you are calculating equipartitioned averages. For example, you could say that you calculate 17 equipartitioned averages from your million data points. The best choice may depend on your audience, but I would understand this expression pretty easily — the name would remind me of the meaning. Constructing a new concept out of existing terms makes it easier to grasp. Perhaps I should add that I give this opinion in the capacity of mathematician and physicist; the Latinist in me only confirms that the word has a Latin origin. Would this be good for your purposes?

• I like this, and agree that it's dangerous (albeit fun) to coin a neologism for a concept that probably already exists. One possible objection: equipartition already has an established meaning that uses a different meaning of partire. It refers to kinetic energy being shared equally, not divided equally. – brianpck Jan 26 '17 at 13:05
• I also like this suggestion. Somehow it does feel a bit better than equinumerous. I don't think the concept already has a name, although I'm sure it is already used. I also posted the question at stats.stackexchange, and it seems like there is no name for it (although I got a good suggestion for a new name also). But I really do need a shorthand to refer to it. @brianpck I think the shared equally in the equipartition theorem is also meant as the energy is split or divided equally. Does not really make sense otherwise. – Lu Kas Jan 26 '17 at 15:45