What seems a simple task but I can't find the right tool to do it. I have a polygon grid cells and say a point feature class. I want to be able to create a table that contains the grid cell ID and for example the sum of points within that cell or the average of the value for those points. For a line feature I would like to simply have a 0/1 value if the line falls into a grid cell. I am doing this in ArcMap 10. This is like Zonal statistics but on a vector layer instead of a raster.

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Your "question" probably evaluates to about 3 questions but the answer to each is roughly the same.

I think there are two tools to look at for transferring your polygon identifier to lines and points:

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