In Section 4.3.3 we noted that spatially extensive variables, such as total population, should not be plotted directly for zones under normal circumstances, but standardized in some manner. An exception to this general rule may be made where cartograms rather than conventional maps are produced (see Section 4.3.4.4). For such maps the areas are distorted in some manner to reflect the (positive) magnitude of an attribute of each region, whilst retaining a sense of the original areal-based map. Densities, with respect to the variable under consideration, thus become uniform in such maps.

For variables that are a subset of a total it is often useful to compute and map these data as a proportion of this total, but for totals themselves we will need to compute a density measure — dividing the total population, N, by the zone area, A. This yields a density value, N/A, for each zone, but assumes that population density is constant through the zone and then may suddenly change to some other value at the zone boundaries. In our discussions on boundaries and on areal interpolation we have already alluded to the inadequacies of simple density calculation, but it remains in widespread use. Conversion of the source dataset to a raster model using some form of intelligent interpolation may well provide a more satisfactory result. A good introduction to mapping density is provided in Mitchell (1999, Chapter 4). Techniques for computing density estimates, including so-called kernel density measures, are discussed in Sections 4.3.4.1 and 0.