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I am working at the scale of 10 square km grid cells for the UK, and have a polygon layer of the Ordnance Survey 10k grid cells in ArcGIS.

I have another layer of the human footprint index, also for the entire UK, that I am using to stratify my data.

However, the resolution of this human footprint index is much greater than that of the 10k grid cells, so I want to aggregate the cells, such that I have a human footprint index value for each 10 sqkm cell.

When I try to do this, however, the squares and grid do not line up - as can be seen in the pictures.

They are in the same projection.

Is there any way to aggregate a layer to the confines of a polygon grid?

Any help would be very much appreciated!

Images here:

Before aggregation
After aggregation

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As suggested by @whuber, please try Zonal Statistics which will require you to use a Spatial Analyst license.

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