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\begin{figure}\begin{center}\BoxedEPSF{Hinges.epsf scaled 750}\end{center}\end{figure}

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 Median). In this ordering,

$\displaystyle H_1$ $\textstyle =$ $\displaystyle a_{n+2}=a_{(N+3)/4}$  
$\displaystyle M$ $\textstyle =$ $\displaystyle a_{2n+3}=a_{(N+1)/2}$  
$\displaystyle H_2$ $\textstyle =$ $\displaystyle a_{3n+4}=a_{(3N+1)/4}.$  

For $N$ of the form $4n+5$, the hinges are identical to the Quartiles. The difference $H_2-H_1$ is called the H-Spread.

See also H-Spread, Haberdasher's Problem, Median (Statistics), Order Statistic, Quartile, Trimean


Tukey, J. W. Explanatory Data Analysis. Reading, MA: Addison-Wesley, pp. 32-34, 1977.

© 1996-9 Eric W. Weisstein