statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, the midhinge is the average of the first and third

quartile In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or ''quarters'', of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a ...

s 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 ''Trimmed'' is a 1922 American silent Western film directed by Harry A. Pollard and featuring Hoot Gibson. It is not known whether the film currently survives, and it may be a lost film. Cast * Hoot Gibson as Dale Garland * Patsy Ruth Miller ...

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 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 ...

; 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 as ...

. :

\operatorname(X) = \overline = \frac = \frac = M_(X)

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 difference ...

(IQR), the difference of the third and first

s (i.e.

IQR = Q_3 - Q_1

), which is a measure of

statistical dispersion In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a Probability distribution, distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard de ...

. 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 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 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 pr ...

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 med ...

(

TM

), which originated in the same context and equals the average of the

median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic fe ...

(

\tilde = Q_2 = P_

) and the midhinge. :

\operatorname(X) = 2 \operatorname(X) - \operatorname(X) = 2 \frac - Q_2

References

{{reflist

External links

H-spread
at

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 Dig ...

Means Exploratory data analysis

See also

References

External links