Hinge
Hinges
The upper and lower hinges are descriptive statistics of a set of N data values, where N is of the form N=4n+5 with n=0, 1, 2, .... The hinges are obtained by ordering the data in increasing order a_1, ..., a_N, and writing them out in the shape of a "w" as illustrated above. The values at the bottom legs are called the hinges H_1 and H_2 (and the central peak is the statistical median). In this ordering,
H_1 = a_(n+2)=a_((N+3)/4)
(1)
M = a_(2n+3)=a_((N+1)/2)
(2)
H_2 = a_(3n+4)=a_((3N+1)/4).
(3)
For N of the form 4n+5, the hinges H_1 and H_2 are identical to the quartiles Q_1 and Q_3. The difference H_2-H_1 is called the H-spread.
See also
H-Spread, Haberdasher's Problem, Hinge Theorem, Order Statistic, Quartile, Statistical Median, TrimeanExplore with Wolfram|Alpha
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References
Tukey, J. W. Exploratory Data Analysis. Reading, MA: Addison-Wesley, pp. 32-34, 1977.Referenced on Wolfram|Alpha
HingeCite this as:
Weisstein, Eric W. "Hinge." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Hinge.html