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I know that they mean more or less the same thing, and in common parlance, they are interchangeable. But from a very strict mathematical sense, is there any difference between the two terms, or are they truly identical synonyms?

LadyCailin
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  • Welcome to Mathematics Stack Exchange. Average is the arithmetic mean; there are other means, such as geometric and harmonic – J. W. Tanner Sep 22 '19 at 20:20
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    https://stats.stackexchange.com/questions/14089/what-is-the-difference-between-mean-value-and-average – Xander Henderson Sep 22 '19 at 20:21
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    If you want to be unambiguous use "arithmetic mean". Average normally means what you think, but is occasionally used (a) wrongly by people who don't know; and (b) in some contexts, correctly (and this will normally be evident from context - either technical, or there are uses in insurance) to denote something other than the arithmetic mean. Make sure you know what you are talking about. If it matters, take care to check what others mean. – Mark Bennet Sep 22 '19 at 20:30
  • I’ve added an average() function to a (general purpose) programming language I’m writing, and in the documentation, I want to be 100% unambiguous, so I just want to make sure my terms are correct and accurate from a mathematical point of view! So I thought it important to research this a little so the documentation is precise. – LadyCailin Sep 22 '19 at 20:42
  • If your goal is to provide good documentation, then you should understand that both "mean" and "average" can carry different meanings, and that there is a significant overlap between the two. Without other context, I would assume that the "mean" is the arithmetic mean (i.e. "add the terms, divide by the number of terms"), but it could also mean the geometric mean, the harmonic mean, as well as notions of mean in statistics (which are related, but relate better to continuous data). – Xander Henderson Sep 23 '19 at 12:58
  • Similarly, "average" typically means the arithmetic mean (or the expected value), but "average" is also sometimes used as a generic term for a measure of central tendency, so it could also mean the median, mode, or some other related measure. If you want to be precise in your documentation, use whichever word you like better, then briefly explain what you mean by that (e.g. "The average() function computes the arithmetic mean of its inputs.") – Xander Henderson Sep 23 '19 at 13:01
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    https://methodscript.com/docs/3.3.4/API/functions/average.html – LadyCailin Sep 23 '19 at 18:52
  • @J.W.Tanner "Average" can have a broader meaning than that. The Wikipedia article lists several types of averages, for example. (Then, "average" is also used in an even broader sense outside of mathematics, such as in "the average person.") – HelloGoodbye Sep 22 '23 at 04:26

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