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Bivariate Extensions of the Boxplot

Kenneth M. Goldberg and Boris Iglewicz
Technometrics
Vol. 34, No. 3 (Aug., 1992), pp. 307-320
DOI: 10.2307/1270037
Stable URL: http://www.jstor.org/stable/1270037
Page Count: 14
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Bivariate Extensions of the Boxplot
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Abstract

The boxplot has proven to be a very useful tool for summarizing univariate data. Several options of bivariate boxplot-type constructions are discussed. These include both elliptic and asymmetric plots. An inner region contains 50% of the data, and a fence identifies potential outliers. Such a robust plot shows location, scale, correlation, and a resistant regression line. Alternative constructions are compared in terms of efficiency of the relevant parameters. Additional properties are given and recommendations made. Emphasis is given to the bivariate biweight M estimator. Several practical examples illustrate that standard least squares ellipsoids can give graphically misleading summaries.

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