Name for particular statistical measure

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Discussion Overview

The discussion revolves around the search for an established name for a statistical measure defined as the arithmetic mean of values that exceed the overall arithmetic mean of a given list of values. The scope includes theoretical considerations and potential applications in statistical reporting.

Discussion Character

  • Exploratory, Debate/contested, Technical explanation

Main Points Raised

  • Some participants inquire about an established name for the arithmetic mean of values greater than the overall arithmetic mean.
  • One participant notes that while they have not heard of such a measure, it is common in statistics to report means for subpopulations, which can provide more informative insights than a single mean.
  • Another participant suggests that the closest related concept might be the median of values greater than the median, referring to it as the third quartile or 75th percentile, and argues that the median is less affected by outliers compared to the arithmetic mean.
  • A participant proposes referring to the measure as a conditional expectation, represented mathematically as ##E[X \vert X\gt \mu]##.
  • Another suggestion is to search for "mean positive deviation" as a related concept when looking for literature on this measure.

Areas of Agreement / Disagreement

Participants do not reach a consensus on an established name for the measure in question, and multiple competing views regarding related concepts and terminology are presented.

Contextual Notes

The discussion highlights various interpretations and related statistical concepts, but does not resolve the question of nomenclature or establish a definitive term for the measure discussed.

onomatomanic
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Given a list of values, one calculates the arithmetic mean of those values which are greater than the arithmetic mean of all values. Is there an established name for that quantity?
 
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onomatomanic said:
Given a list of values, one calculates the arithmetic mean of those values which are greater than the arithmetic mean of all values. Is there an established name for that quantity?

I've never heard of such a thing, but in reporting many types of statistics, such as income, it's common to divide the population into subpopulations (often quintiles, for some reason) and give the mean for each subpopulation separately. That gives a lot more information than just given means, because a single billionaire can skew the mean.
 
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onomatomanic said:
Given a list of values, one calculates the arithmetic mean of those values which are greater than the arithmetic mean of all values. Is there an established name for that quantity?

Closest thing is the median of the values that are greater than the median.
That is the third quartile, or 75th percentile.
The median is usually close to the arithmetic mean, and in particular it is not noticeably impacted by stevendaryl's single billionaire.
The cases where the median is significantly different from the arithmetic mean, are the cases where we shouldn't use the arithmetic mean.

I believe there is no word for the arithmetic mean of the values greater than the arithmetic mean.
 
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you could call it a conditional expectation, like ##E[X \vert X\gt \mu]##
 
onomatomanic said:
Is there an established name for that quantity?

If your goal is to look up articles about such a measure, search on "mean positive deviation", which is a related concept.
 

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