# Obtain normalized raster average per polygon?

I have a raster that contains percentages of total forest killed plus a polygon layer that defines different zones. My goal is to find a good statistical representative that describes the forest killed situation per zone. So what I did first is I used zonal statistics as table with the raster as the input raster and the zones as polygons as the feature zone. This calculated me an average per zone based on the raster cells in the zone. However, this destorts the result. One zone might only have 5 raster cells in there but all of these cells have a value of 50%, which gives me an overall average of 50% for this zone. Another zone might have 1000 raster cells and obtains also an overall average of 50%. So that doesn't show that the latter zone has more raster cells with fores killed. So I need to normalize it somehow. What I thought I could do is try and calculate a weighted average. So I would need to know how many raster cells there are in total and how many cells there are within each zone. With that I could divide the amount of raster cells per zone by the total amount of raster cells in the whole region and then times that by the average of the raster cells per zone?

Is that the right approach to not misrepresent the data? Also...how would I do that in ArcMap10??

• What value does an individual pixel have in your raster and what does it specifically represent? What is the spatial resolution of your raster data? – Aaron Dec 5 '12 at 1:22
• An individual cell of the raster represent a percentage from 1-100% of total forest killed. The cell size is 100mx100m. Why does zonal statistics as table not offer a simple count? – Sandra Dec 5 '12 at 1:27
• Sandra, zonal stats should offer a count. If it does not, then perform zonal stats using a constant grid of unit values: the sum equals the count. By the way, people appreciate it when you provide feedback on answers to your questions (by voting up decent ones and accepting the best when they merit it): this helps newcomers identify the better answers. Please take a moment to do this for your previous questions. – whuber Dec 5 '12 at 1:57
• Thanks for pointing that out whuber. I went through my questions and rated and accepted them. Regarding the zonal stats as table, you are right it does give me a count. Unfortunately, that count seems to be wrong? If I double check some regions, I count zero raster cells but the zonal stats table output tells me that there are 16? It shouldn't be a projection issue, since both datasets are in the same projections. Any other ideas? – Sandra Dec 5 '12 at 18:57

## 1 Answer

I think you can normalize the averages by zone areas. Before doing Zonal Statistics as Table, just calculate areas of the polygons in their attribute table. Check if your polygons are projected. Then you can just divide average percentage by the zone area. I think it is a little more precise than pixel count.