In
statistics, the midhinge is the average of the first and third
quartiles and is thus a measure of
location
In geography, location or place are used to denote a region (point, line, or area) on Earth's surface or elsewhere. The term ''location'' generally implies a higher degree of certainty than ''place'', the latter often indicating an entity with an ...
.
Equivalently, it is the 25%
trimmed mid-range
In statistics, the mid-range or mid-extreme is a measure of central tendency of a sample defined as the arithmetic mean of the maximum and minimum values of the data set:
:M=\frac.
The mid-range is closely related to the range, a measure of ...
or 25%
midsummary; it is an
L-estimator
In statistics, an L-estimator is an estimator which is a linear combination of order statistics of the measurements (which is also called an L-statistic). This can be as little as a single point, as in the median (of an odd number of values), or a ...
.
:
The midhinge is related to the
interquartile range (IQR), the difference of the third and first
quartiles (i.e.
), which is a measure of
statistical dispersion
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile ...
. The two are complementary in sense that if one knows the midhinge and the IQR, 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
In statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but pri ...
in the late 1970s,
[Tukey, J. W. (1977) ''Exploratory Data Analysis'', Addison-Wesley. ] and "midhinge" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the
trimean 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:
: TM= \frac
This is equivalent to the average of the m ...
(
), which originated in the same context and equals the average of the
median (
) and the midhinge.
:
See also
*
Interquartile mean
*
L-estimator
In statistics, an L-estimator is an estimator which is a linear combination of order statistics of the measurements (which is also called an L-statistic). This can be as little as a single point, as in the median (of an odd number of values), or a ...
References
{{reflist
External links
H-spreadat
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Di ...
Means
Exploratory data analysis