# What is the terminology for data aggregated via summed totals versus data aggregated via means?

The two types of data differ in that if you decide to decrease the temporal (time) resolution of the first type of data you take the mean of lower the resolutions. With the second you take the sum over the lower resolutions. Here is a concrete example

Gas Used (kWh), Outside Air Temperature (C), Time Resolution (Minutes)
100, 20, 20
140, 22, 20
120, 21, 20


Here the hourly (60 Minute) resolution data is clearly

360, 21, 60


and is found by averaging the temperature and summing up the gas used.

What I really wish to know is what the names for each of these types of data are called. I understand that this question is not the best but it is hard to ask a question about something whose names you do not know. If you have a better way of articulating the question then please go ahead and edit it.

Properties that are physically additive are called extensive. Mass is extensive, as when you add (literally!) weights to a balance.

A feature of extensive properties is that totals make sense. In your example, gas used, measured in kWh, is one instance.

The word physically is not meant restrictively here. My income in April and my income in May can be added, as can my expenditures. Both are extensive properties. So, there are other non-physical situations in which addition makes sense.

If totals make sense, then means make sense too. Whether they are the measures you want to use, however, depends on your purpose.

Otherwise properties that are not physically additive are called intensive. Temperature is intensive. If you mix bodies, the resulting temperature is some kind of weighted mean, and certainly not the total.

This Wikipedia article says much more from a physical science point of view.

One source emphasising the importance of this distinction in statistical science is Cox, D.R. and Snell, E.J. 1981. Applied statistics: principles and examples. London: Chapman and Hall. See p.14. (They use the term non-extensive, which I do not find attractive.)

• +1 Wow, this is interesting! I was just gonna suggest "temporal aggregation" but your angle is probably closer to the question. – Penguin_Knight May 28 '15 at 16:20
• In a classification perhaps more widely known, I think it follows that as extensive variables must have true zeros, they must be ratio scale, but the converse isn't true. – Nick Cox May 28 '15 at 16:29
• A nice answer. It seems strange that I have never encountered these words in this context before. As they provide important concepts regarding data it does strike me as worrying that they are not more widely known or at least distinguished between. I know it is not just me as have asked my collogues this question and we all work with data to some level! – josh May 29 '15 at 8:30
• I share your puzzlement. I don't see the distinction often being made in statistical literature at all, certainly not compared with the over-worked nominal-ordinal-interval-ratio distinctions. Sir David Cox's later book with Christl Donnelly I think returns to the point. (Sir David and I are not knowingly related.) – Nick Cox May 29 '15 at 8:44
• Yes. I did think to myself, "is this his father?". Haha. Also, is there a better way to re-write the title so that people my find the answer to this question more easily? – josh May 29 '15 at 9:56

In database applications/data warehouse/BI it is common to refer to additive measures