# Need help choosing appropriate weighted average (noble cause)

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.

For example.

• 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.

• You seem to be over-thinking this. If you have information for each house in your "grouping", then average those distances to get the average distance from house to school. You can then compare with those for houses in other groupings. The density of houses around mine is irrelevant to my distance to school. Each house's distance is what it is. What you may need is some weighting for people (children?) in each house. – Nick Cox Feb 12 at 18:46