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If I have a map of the U.S. with individual polygons at the county-level, and then in another layer, a set of points of interest, is there a way to tabulate how many POI per each polygon ("county") and export that data? I'd like to create a histogram showing how many POI per county there are for all counties.

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You should do a spatial join and join the polygon id to the points. Right click on the point layer in your table of contents and select join. Make sure its a spatial join and you joining Polygons to Points, also make sure each point gets the attributes of the polygon it is in (not nearest too)

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Once this is done you will have a new featureclass that holds your points with an attribute showing which polygon it is in. You will then use Summarize (right click on the field you want summarized in the attribute table and summarize on the field that holds the polygon ID. This will give you a total count of points in the poly.

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You can use a tool that calculates the count of points inside polygon, even using a buffer. e.g. Using this tool you can count the number of points that fall inside the polygon itself and 300m buffer. If you want to calculate just the polygon and no buffer then set search radius to 0m.

demo

Details of the tool can be found here.

Usage: Just locate the tool in the arc catalog and use.

Tool download link

N.B. You are welcome to suggest on this tool. I will try to incorporate your suggestions.

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There are some methods to do it. If your poi's do not have a unique ID to join the Counties then :

You can use spatial join .The target feature is POI's and the join features is counties. The result of spatial join is POI features that have attributes of counties. Then use summary statistics on join result and summarize your data based of desired fields.

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