# How can I map polygon value distribution?

I'm surveying an area and have a z-value attached to each polygon. In comparison to the area I'm studying the polygons are quite small. What I'm trying to do is show the distribution of this value. I've been researching IDW, heatmapping and Kriging but none of these seem to quite fit the purpose. The main problem I've come upon so far is by using the centroids, which aren't evenly distributed, I am analysing more that spatial distribution than the value distribution. I'm hoping to produce a raster output, purely on a visual basis as they show the spread clearly. If anyone has any suggestions of tools, techniques or even advice on where to start looking, I would be more than happy for your help. I'm using QGIS mainly, but also have access to ArcGIS and some other pieces of software.

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What kind of data are these? Your analyses and cartographic choices ought to depend on whether the data represent a sample or an exhaustive set of values, are discrete or not, ordered or not, what kind of polygonal property they represent (such as a total, average, value at some central point, or some other kind of summary), the nature of any measurement errors, and more. – whuber Nov 30 '12 at 17:28
Basically I have polygons, designed to contain a population of 1000-3000 people, with total population values and an additional numerical variable, which is what is aimed to be visualised. After looking some more, a combination of chloropleth, using ArcGIS 10.1, and population weighted cartograms, using ScapeToad, seemed the best option to demonstrate the values in the dataset. The chloropleth shows the actual geographical distribution while the chloropleth removes any low density areas, both showing the same classes for the other variable. – dlovett Feb 13 '13 at 14:10
A choropleth of population density is an excellent choice. A choropleth of the actual population would be deceiving, because it confounds population with the polygon size. Polygon sizes are usually artifacts of relatively arbitrary or irrelevant decisions related to administration of the area or collecting the data. – whuber Feb 13 '13 at 14:54
I agree a chloropleth of total population wouldn't be the best idea. Though I think I may need to clarify. The data I am representing is the other variable, number of people from that polygon using a service. These polygon sizes have been specifically designed to be as close to a mean population size as possible. As such, as the population density increases the polygon size decreases, IDW or Kriging in this case would show population density, if population was the variable being mapped. – dlovett Feb 13 '13 at 15:02