A fourth type of average?

[Pfhorrest]

Is there a name for ([highest value] + [lowest value] / 2)? That's not the mean, median, or mode (unless you only have two members in the set you're measuring). But it seems like that's some kind of "average" in a sense that might be useful on some occasions.

[ConMan]

In statistics, the mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

It's not particularly useful, although it is related to the German tank problem which is one of my favourite statistics stories.

[Soupspoon]

It's also the antithesis of the Winsorised value, a potentially problematic (composite) value to which Winsorising is the solution and a solution to some of the potential problems of the Winsorisish issues. Mathematically, it's interesting to observe as the key to the recursive offset each time you progressively clip extremes off the sequence to see what sort of curve you get betwixt mean (or, in some odd cases, mode) and median. Which can sometimes tell you things about the set generation, alongside analyses for Benford's Law, etc.

[ucim]

it's interesting to observe as the key to the recursive offset each time you progressively clip extremes off the sequence to see what sort of curve you get

Sounds like you want a violin plot. Or a viola plot.

Jose

[Soupspoon]

it's interesting to observe as the key to the recursive offset each time you progressively clip extremes off the sequence to see what sort of curve you get

Sounds like you want a violin plot. Or a viola plot.

I was thinking more a Banjo-Didgeridoo-Saxophone-Marimba plot.

[DavCrav]

The fourth type of average would I guess be the geometric mean, assuming that the arithmetic mean was your other one. If not, then you should read them the other way round.

[doogly]

You do not have to assume the other ones, they're right there in the first post.

Shoutout to the harmonic mean also, while we're at it.

[Soupspoon]

Mr Mean

[doogly]

Mr Mean

Not to be confused with Mr Green

[Eebster the Great]

While we're at it, nobody seems to have mentioned that the technical term for what Pfhorrest calls an "average" is a "measure of central tendency," and there are many such examples, a few of which are listed in the corresponding Wikipedia article.