A fourth type of average?

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Pfhorrest
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A fourth type of average?

Postby Pfhorrest » Tue May 15, 2018 12:50 am UTC

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.
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Re: A fourth type of average?

Postby ConMan » Tue May 15, 2018 1:39 am UTC

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Re: A fourth type of average?

Postby Soupspoon » Tue May 15, 2018 6:47 am UTC

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.

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Re: A fourth type of average?

Postby ucim » Wed May 16, 2018 12:00 am UTC

Soupspoon wrote: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.

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Re: A fourth type of average?

Postby Soupspoon » Wed May 16, 2018 12:01 pm UTC

ucim wrote:
Soupspoon wrote: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.

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Re: A fourth type of average?

Postby DavCrav » Fri May 18, 2018 8:04 pm UTC

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.

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Re: A fourth type of average?

Postby doogly » Mon May 21, 2018 12:42 pm UTC

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.
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Re: A fourth type of average?

Postby Soupspoon » Mon May 21, 2018 2:06 pm UTC


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Re: A fourth type of average?

Postby doogly » Mon May 21, 2018 2:10 pm UTC

Soupspoon wrote:Mr Mean

Not to be confused with Mr Green :mrgreen:
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Re: A fourth type of average?

Postby Eebster the Great » Mon May 21, 2018 5:57 pm UTC

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.


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