High School Name for particular statistical measure

[onomatomanic]

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?

 

[stevendaryl]

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.

 

[I like Serena]

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.

 

[StoneTemplePython]

you could call it a conditional expectation, like $E[X \vert X\gt \mu]$

 

[Stephen Tashi]

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.