Midhinge

In statistics, 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.

The midhinge is complemented by the H-spread, or interquartile range, which is the difference of the third and first quartiles and which is a measure of statistical dispersion, in sense that if one knows the midhinge and the interquartile range, one can find the first and third quartiles.

The use of the term "hinge" for the lower or upper quartiles derives from John Tukey's work on exploratory data analysis, 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 and the midhinge.

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