## 10 Derivatives from Digital Boundaries – Centroids

During the course of this module we have seen how specific instances of geographies held within a digital boundary dataset are normally held as a polygon. Synonymous with the polygonal representation of a geographic region is the centroid. A centroid is a point that acts as an approximation of regions geography. When you use digital boundary data, particularly that from the census you may find yourself coming across population-weighted and geometrically-weighted centroids.

What is the difference between these?. Consider the image below. This shows a polygon that represents the extent of a 2001 census Output Area. Also shown are two points. These are a population-weighted and geometrically-weighted centroid representation of the Output Area. Geometrically-weighted centroid locations are computed algorithmically as a derivative of the polygons geometry. Usually the algorithm includes checks to ensure that the final location of the centroid falls inside the area of the polygon. If this does not happen then this leaves the possibility for error to be introduced into subsequent use of the data. Population-weighted centroid locations tend not to take the polygon geometry into account. The location of the centroid is positioned so that it lies closest to the densest occurrence of population within the region bound by the polygon. This is to ensure that the simple point representation corresponds as accurately as possible to the population on the ground that the OA represents.

Often Population and Geometric weighted centroids are added to digital boundary datasets as attributes. Here we see an example from 2001 Census Output Areas:

In this case PopEast; PopNorth taken together provide the location of the population weighted centroid wheras GeoEast and GeoNorth taken together provide the location of the geometrically weighted centroid.

The above map shows a highlighted record in the 2001 Census Output Areas. You can see the record highlighted in the attribute table of the DBD (yellow) and on the map (blue outline). The attribute table shows that the record contains attributes providing details of the population (through popeast and popnorth) and geometrically weighted (through geoeast and geonorth) centroid locations. These locations are shown on the map. Green triangles are Population-weighted centroid locations. Red triangles are Geometrically-weighted centroid locations. You can see that for the higlighted polygon, the geometrically weighted centroid lies close to the centre of the polygon wheras the population-weighted centroid is closer to population at North-East of the polygon. We know this is where most of the population is located due to the increase in density of the neighbouring Output Areas. This same distribution applies to many of the other Output Areas nearby