Trimean
Encyclopedia
In statistics
the trimean (TM), or Tukey's trimean, is a measure of a probability distribution
's location
defined as a weighted average of the distribution's median
and its two quartiles:
This is equivalent to the average of the median
and the midhinge
:
The foundations of the trimean were part of Arthur Bowley's teachings, and later popularized by statistician John Tukey
in his 1977 book which has given its name to a set of techniques called Exploratory data analysis
.
Like the median and the midhinge, but unlike the sample mean, it is a statistically resistant L-estimator with a breakdown point of 25%. This beneficial property has been described as follows:
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
the trimean (TM), or Tukey's trimean, is a measure of a probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
's location
Average
In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....
defined as a weighted average of the distribution's median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
and its two quartiles:
This is equivalent to the average of the median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
and the midhinge
Midhinge
In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location.Equivalently, it is the 25% trimmed mid-range; it is an L-estimator....
:
The foundations of the trimean were part of Arthur Bowley's teachings, and later popularized by statistician John Tukey
John Tukey
John Wilder Tukey ForMemRS was an American statistician.- Biography :Tukey was born in New Bedford, Massachusetts in 1915, and obtained a B.A. in 1936 and M.Sc. in 1937, in chemistry, from Brown University, before moving to Princeton University where he received a Ph.D...
in his 1977 book which has given its name to a set of techniques called Exploratory data analysis
Exploratory data analysis
In statistics, exploratory data analysis is an approach to analysing data sets to summarize their main characteristics in easy-to-understand form, often with visual graphs, without using a statistical model or having formulated a hypothesis...
.
Like the median and the midhinge, but unlike the sample mean, it is a statistically resistant L-estimator with a breakdown point of 25%. This beneficial property has been described as follows: