Geographic Box Plots

Abstract

Traditional box plots, described by Tukey in 1977, can be biased representations of geographic or spatial variables, since they do not take into account the areas associated with the elements of geographic variables. To help solve this problem, we propose and evaluate a spatially (areally) weighted box plot, a "geographic box plot," that can be used to describe a wide variety of geographic variables. Much of our discussion of box plots also applies to "traditional" and "geographic" histograms and percentile plots. Traditional and geographic box plots of one hypothetical and two real-world geographic variables are constructed and compared to illustrate our points, as well as to illustrate the often marked differences between traditional and geographic box plots of the same geographic variables. The real-world geographic variables considered here are human population density (in the year 2000) within the contiguous 48 United States and five-year-average (January 2001-December 2005) air temperature over the Arctic land surface. Our traditional box plot of population density over represented the small, high-density states, whereas our corresponding geographic box plot correctly depicted the geographic distribution of population density. A geographic box plot correctly accounted for the reduction in spherical grid-node areas with latitude over the Arctic land surface, whereas a traditional box plot of the spherical grid-node values did not. Our hope is that geographers and other scientists will make refinements to and find many more applications for our geographic box plots.