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Midhinge

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Instatistics, themidhinge (MH) is the average of the first and thirdquartiles and is thus a measure oflocation.Equivalently, it is the 25%trimmed mid-range or 25%midsummary; it is anL-estimator. The midhingeMH is defined as ${\begin{aligned}\operatorname {MH} (X)&={\overline {Q_{1,3}(X)}}\\&={\frac {Q_{1}(X)+Q_{3}(X)}{2}}\\&={\frac {P_{25}(X)+P_{75}(X)}{2}}\\&=M_{25}(X).\end{aligned}}$

The midhinge is related to theinterquartile range (IQR), the difference of the third and firstquartiles (i.e.IQR =Q₃ −Q₁), which is a measure ofstatistical dispersion. The two are complementary in sense that if one knows the midhinge and theIQR, one can find the first and third quartiles.

The use of the termhinge for the lower or upper quartiles derives from John Tukey's work onexploratory data analysis in the late 1970s,^[1] andmidhinge is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than thetrimean (TM), which originated in the same context and equals the average of themedian (~X =Q₂=P₅₀) and the midhinge: ${\begin{aligned}\operatorname {MH} (X)&=2\operatorname {TM} (X)-\operatorname {med} (X)\\&=2\;{\frac {Q_{1}+2Q_{2}+Q_{3}}{4}}-Q_{2}.\end{aligned}}$

See also

References

^Tukey, J. W. (1977)Exploratory Data Analysis, Addison-Wesley.ISBN 0-201-07616-0

External links

H-spread atMathWorld

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