In
statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, 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 or 25%
midsummary; it is an
L-estimator
In statistics, an L-estimator (or L-statistic) is an estimator which is a linear combination of order statistics of the measurements. This can be as little as a single point, as in the median (of an odd number of values), or as many as all points ...
. The midhinge is defined as
The midhinge is related to the
interquartile range
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the differen ...
(), 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 interquartil ...
. The two are complementary in sense that if one knows the midhinge and the , 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 Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...
's work on
exploratory data analysis
In statistics, exploratory data analysis (EDA) is an approach of data analysis, analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or ...
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 (), which originated in the same context and equals the average of the
median
The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “ ...
( ) and the midhinge:
See also
*
Interquartile mean
*
L-estimator
In statistics, an L-estimator (or L-statistic) is an estimator which is a linear combination of order statistics of the measurements. This can be as little as a single point, as in the median (of an odd number of values), or as many as all points ...
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 ...
Means
Exploratory data analysis