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In teaching descriptive statistics, measures of central tendency come up early on, e.g. before measures of spread. For me it is natural enough to learn about central tendency, or location, of the data before learning many other properties, but this just might be stemming from how I was taught.
However, is there any good motivation for why the central tendency should be the first thing one would learn about?

I guess one cannot say that a certain measure of central tendency (such as mean, median or mode) contains the most information about the data; nor could one say that it contains the most important information (because the relative importance really depends on what the intended use of the data is).
But then what could be said instead?

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  • $\begingroup$ An argument has been made that in order to teach spread we need to teach central tendency first, because the definition of the former depends on the definition of the latter. But what about the importance of central tendency? Do we teach central tendency first just to have a good basis for teaching spread? Is central tendency not of primary interest in itself? $\endgroup$
    – Richard Hardy
    Sep 5, 2018 at 12:14
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    $\begingroup$ Of course it's of primary interest. Many people arrive at their statistics education without any quantitative habits of thought. They are perfectly willing to say "my pet is large" or "the distance is short" without recognizing that these are essentially meaningless statements. The very first thing anybody should want to know about an unfamiliar dataset would be "what kinds of numbers are in it?"--exactly how much do the pets weigh and just what are the distances? Just knowing the typical pet weight is 10 grams and a short distance is 100 parsecs tells you a lot! $\endgroup$
    – whuber ♦
    Sep 5, 2018 at 12:18
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    $\begingroup$ @whuber, a great point. Putting it in general terms could make for a good answer, I think. (I do appreciate concrete examples, but here I would like to formalize what they are intended to convey.) $\endgroup$
    – Richard Hardy
    Sep 5, 2018 at 12:38
  • $\begingroup$ Often the primary interest is in somen comparison. Maybe we should start there? $\endgroup$
    – kjetil b halvorsen ♦
    Oct 5, 2020 at 3:59

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One reason we teach measures of central tendency before measures of spread because many measures of spread involve measures of central tendency: The standard deviation involves the mean, median absolute deviation involves the median. We could teach the range without teaching the mean, but teaching range is not exactly a long term project.

Indeed, the mean is used nearly everywhere in statistics.

Among measures of central tendency, I think we teach the arithmetic mean first because it is familiar - "average" occurs all over the place and it usually means "arithmetic mean".

Of course, there are lots of measures of central tendency that we often do not teach so early in the curriculum - e.g. the trimmed, winsorized, geometric and harmonic means.

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  • $\begingroup$ Thank you for your answer. But what about the importance of central tendency? Do we teach central tendency first just to have a good basis for teaching spread? Is central tendency not of primary interest in itself? $\endgroup$
    – Richard Hardy
    Sep 5, 2018 at 12:39
  • $\begingroup$ Well, sure, central tendency is important. But the question was about why teach it first and, specifically, before measures of spread. $\endgroup$
    – Peter Flom
    Sep 5, 2018 at 13:25
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    $\begingroup$ I understand. The question was indeed about why teach it first, not why teach it before something else. I mentioned measures of spread just to illustrate that there are other things that follow measures of central tendency; I did not intend to make the question about which of the two should be taught first. Rather, I am interested in why measures of central tendency should be taught first regardless of what follows next, and an example of an intuitive answer to the intended question is whuber's comment, though he uses rather specific examples rather than distilling the essence to abstractions. $\endgroup$
    – Richard Hardy
    Sep 5, 2018 at 13:32
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    $\begingroup$ While in this case (and surely in many others) it is easier to express the idea in terms of examples as @whuber did, I'd say central tendency is taught first exactly because it can convey an image for the typical, i.e. central, behavior, i.e. tendency, of the object (be it empirical, such as data, or theoretical, such as a random variable) within only one measure. This is attractive because it simplifies things, but of course the quality of that measure quickly arises as the next topic. $\endgroup$
    – Emil
    Sep 5, 2018 at 15:30

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