Name for particular statistical measure

In summary, the conversation discusses the concept of finding the arithmetic mean of values that are greater than the overall arithmetic mean. This is often used in reporting statistics such as income, where subpopulations are divided and their respective means are given. The closest term for this quantity is the third quartile or 75th percentile, and it can also be referred to as a conditional expectation or "mean positive deviation". However, there is no established term for this specific measure.
  • #1
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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  • #2
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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  • #3
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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  • #4
you could call it a conditional expectation, like ##E[X \vert X\gt \mu]##
 
  • #5
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.
 

What is the mean?

The mean, also known as the average, is a measure of central tendency in a set of numerical data. It is calculated by adding all the numbers in the data set and dividing by the total number of values.

How is the median calculated?

The median is the middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.

What is the purpose of calculating the mode?

The mode is the most frequently occurring value in a data set. It can provide information about the most common value or category in the data, which can be useful for making comparisons or identifying patterns.

Why is standard deviation important?

Standard deviation is a measure of how spread out the data is from the mean. It is important because it can help determine the reliability of the data and how much the individual values may vary from the average.

How is correlation measured?

Correlation is a measure of the relationship between two variables. It is typically measured using a correlation coefficient, with values ranging from -1 to 1. A higher absolute value indicates a stronger relationship between the variables.

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