The Geo-boxplot. A tool for spatial synthesis

Abstract

The Boxplot is a statistical tool based on the fundamental characteristics of a distribution. Introduced by Tukey in 1969, it is widely used for its great strength of exemplification. As known, the graph shows a rectangle (Box) with limits placed on the first and third quartiles; deviations from the median and extreme values ​​are also identified, to immediately display a summary of the shape of the distribution. Using geographic data, this brief note discusses the possibility of making a similar representation capable of exploiting the geographic element. This reasoning is based on the introduction of a cumulative function of the geographic data values ​calculated on the distance from a predetermined point. Once the cumulative frequency has been valued, it is possible to consider the concept of "deep average" introduced by Tukey himself for the Bagplot, which allows to divide the plane of the bivariate distribution into two equal parts. This tool can also be developed in an ArcGIS environment where, after defining a representative point of a geographical distribution - the median center – the tool allows to divide the observations into two equal parts according to their functional distance from this point. Such graphical representations allow to compare different phenomena occurring in the same places and summarise them using geographical concentration indicators.