Find average density value within a polygon in ArcMap

I've created a point density heat map for a city intended to show areas where there is more or less access to a certain type of public school.

It would be useful to be able to identify which local political districts have the greatest or least access (by proximity) to this type of school. Important here is not just measuring distance to any one school (as in distance to closest point). Rather, access to multiple schools (i.e. greater density) should be rewarded. I want to be able to say something like, "students in District A wishing to attend a school like this have, on average, more nearby options than students in District B." Schools don't need to be in a particular district to be considered an option for the students in that district (so points outside a particular polygon can be considered). In the end, I want some kind of rank or value to compare the districts.

Any suggestions? Looking at the heat map, something equivalent to the average density value would make sense, but maybe there's another tool?

Extra great would be the ability to weight by population density somehow (maybe by census tract)?

I'm using ArcMap 10.3.1

Here's a screenshot of the raster heat map, with political district shapefile overlaid:

• So just to clarify, you have both 1) a raster layer heat map that shows the average distance to the nearest school, and 2) a layer of polygon zones with population information? Or is the 1st element not quite there yet? Commented Oct 10, 2017 at 20:23
• Also, if you can post a screenshot of that heatmap or the points used to create it, this should be a pretty easy-to-accomplish task. Commented Oct 10, 2017 at 20:26
• Thanks @map. 1) the heat map just shows density; 2) the polygon zones don't have distributed population information within them, just pop attributes for each one, if that makes sense. I edited the orig post to include the screenshot. Commented Oct 11, 2017 at 15:09

I'm not exactly sure which statistic would be most useful to you but it sounds like a good use for Zonal Statistics as Table.

I would use the polygon layer for the zone layer and the density raster as the value layer. You could use a max value within a polygon or an average or a normalized average.

The question isn't specific but Zonal Statistics as Table would be flexible to provide a few ways of looking at the question. This requires Spatial Analyst but if you used the Point Density tool, you already indicated that you have that.

If you'd like you can also use the tabular output to join back to the original polygon layer to symbolize the result(s).

• Thanks @jbchurchill, that worked pretty well! Using that method, I was able to get a mean value for each district, which is what I was after. I guess if I wanted to factor in population, I'd need to have something like a weighted point density raster that somehow figures in population, but I don't know if that's a thing. Marking this as solved as it answered my basic question. Commented Oct 12, 2017 at 16:25
• You are welcome! - Having population in the polygon layer could be useful too as something to normalize your density by in the symbology. Commented Oct 12, 2017 at 17:57

I suggest an easy workflow in model builder or small code Arcpy. It is even manually doable, if there is a minimal number of polygon to process.

1. Polygon selection;
2. Clip raster based on the strict polygon delineation;
3. Compute the average of the clipped raster;
4. Save the average value with Id of the polygon.

Loop over other polygons.

Join the list of average value with Id of the polygon to you table.

I have already coded in OGR and GDAL.