Name for particular statistical measure

  • #1
103
1
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?
 

Answers and Replies

  • #2
stevendaryl
Staff Emeritus
Science Advisor
Insights Author
8,919
2,904
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.
 
  • Like
Likes FactChecker
  • #3
I like Serena
Homework Helper
6,579
176
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.
 
  • Like
Likes FactChecker
  • #4
StoneTemplePython
Science Advisor
Gold Member
1,203
596
you could call it a conditional expectation, like ##E[X \vert X\gt \mu]##
 
  • #5
Stephen Tashi
Science Advisor
7,703
1,513
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.
 

Related Threads on Name for particular statistical measure

Replies
0
Views
5K
Replies
1
Views
2K
Replies
3
Views
3K
  • Last Post
Replies
4
Views
2K
Replies
2
Views
2K
Replies
1
Views
832
Replies
2
Views
2K
Replies
1
Views
6K
  • Last Post
Replies
1
Views
719
Top