# Calculating area weighted average of attribute in one layer by shape in another using ArcGIS for Desktop?

For a project I am working on I would like to intersect fire station response districts with income data to determine the median income per response district. However the borders of the layers obviously do not line up. What is the best method to go about manipulating the data to have the output show the median income based on the response districts?

I am using ArcMap 10.2.2 for this analysis. I have a polygon shapefile with median income information and a polygon shapefile of fire stations first in response areas.

• Welcome! I suggest you a add some more information about your tools (QGIS/ArcGIS or other) and your data sets (shapefiles or other). The projections of your source data might be an issue as well, so I would suggest you also elaborate on this issue. The last question is really a different question. Elaborate some and you will get more attention to your question. Commented Feb 25, 2015 at 22:16
• How badly do the not line up? Statistics do some funny things in intersections; If the median income is X in a polygon it's still X even when it's cut in half, all you need to work out is how to weight the statistics of the districts based on shape.area when calculating the mean within that area, this may be better done in Excel as a pivot table, you can open the dbf of the shape but DON'T SAVE THE DBF file with Excel - it will break the shapefile. Commented Feb 25, 2015 at 23:25
• They are pretty far off with fire station districts sometimes covering multiple pieces of different income level polygons. Example: 75% of Fire Station 1's district may overlay a polygon whose median value is \$X, then 12.5% overlays an area where median income is \$Y and 12.5% overlays median income is \$Z. I want to see if there is some way to weight these or manipulate these where the output shows one total for Fire Station 1's district. Ratio policy comes to mind, but since it is not number of people making said income but rather just the median value, I don't know if that is correct. Commented Feb 25, 2015 at 23:31
• You are correct that Ratio Policy isn't what you want to use. You've got a constant value throughout the shape (aka, normalized value meaning it's already taken area into account), so apportionment, or dividing that value up by area, doesn't make sense. As you say, if you had population then you'd want to split that value up by area (lacking any distribution info and so assuming uniform distribution). Commented Feb 25, 2015 at 23:54