We are lobbying our council to open a primary school in our area, and I'm trying to demonstrate the need.
I have location information for all houses and schools in the county, I can calculate distances to the nearest schools, and I have a natural grouping for the properties. What I'm hoping to demonstrate is that, for our grouping, the local cluster of properties has a higher than normal average distance to the nearest school.
If there is a single property 20km from a school, well bad luck for them but it's not significant - it's a high average, but a low total distance for all the residents (because of the low density and small dataset)
If there are 5000 houses 500m from a school, well that's fine too - it's a low average, although a high total distance due to the density.
In our case (900 houses 5km from a school) we have a largish group which is relatively dense - i.e. all members have low distance to their geographic centroid - there's a high distance from each member to the school.
I'm certain there is a model I should be using that caters for both average distance and density, I have a suspicion that it will involve a gaussian distribution, but I'm not sure what, and I'm reluctant to bodge this as I have to present this argument to the council in a few weeks. Any pointers would be very helpful.