Midhinge
Encyclopedia
In statistics
, the midhinge is the average of the first and third quartile
s and is thus a measure of location
.
Equivalently, it is the 25% trimmed
mid-range; it is an L-estimator.
The midhinge is complemented by the H-spread, or interquartile range
, which is the difference of the third and first quartile
s and which is a measure of statistical dispersion
, in sense that if one knows the midhinge and the interquartile range, one can find the first and third quartiles.
The use of the term "hinge" for the lower or upper quartiles derives from John Tukey
's work on exploratory data analysis
, and "midhinge" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean
, which originated in the same context.
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 midhinge is the average of the first and third quartile
Quartile
In descriptive statistics, the quartiles of a set of values are the three points that divide the data set into four equal groups, each representing a fourth of the population being sampled...
s and is thus a measure of location
Location parameter
In statistics, a location family is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter μ, which determines the "location" or shift of the distribution...
.
Equivalently, it is the 25% trimmed
Trimmed estimator
Given an estimator, a trimmed estimator is obtained by excluding some of the extreme values. This is generally done to obtain a more robust statistic: the extreme values are considered outliers....
mid-range; it is an L-estimator.
The midhinge is complemented by the H-spread, or interquartile range
Interquartile range
In descriptive statistics, the interquartile range , also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles...
, which is the difference of the third and first quartile
Quartile
In descriptive statistics, the quartiles of a set of values are the three points that divide the data set into four equal groups, each representing a fourth of the population being sampled...
s and which is a measure of statistical dispersion
Statistical dispersion
In statistics, statistical dispersion is variability or spread in a variable or a probability distribution...
, in sense that if one knows the midhinge and the interquartile range, one can find the first and third quartiles.
The use of the term "hinge" for the lower or upper quartiles derives from 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...
's work on 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...
, and "midhinge" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean
Trimean
In statistics the trimean , 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:...
, which originated in the same context.