dividing a total "count" by an areal extent will give you a relative measure of your variable.
the final units are aka density.Density is a relationship.
in arcGIS 10.1 , you use Layer Properties to draw quantities using symbol size to show relative value by chooosing the appropriate fields for both Value and Normaliztion.
Larger areas may or may not influence the numerical values you want to classify. What you are doing in this calcaulation is deriving spatially intensive data from spatially extensive data. dividing one sum (as in, summary statistic) by another sum will yield you a spatially independent (of size) unit. Note that areas and perimenters are also considered summary statistics.
if you split the areal unit and recalulate (but first you make the basic assumption that the counts are uniformly distributed across the area), the density value will remain the same as before but the counts and the area will not say the same. Proportions, though calulated differently than density, are also spatially extensive.
spatially extensive data should not be used to symbolize a chorolpleth map although this mistake is made over and over again by the uninitiated
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