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I have a raster layer containing the elevation info., and another gridded layer (shapefile type). What I want to do is to calculate the mean elevation within each grid to have a single representative value.

Does anyone know how to handle this?

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In ArcGIS Desktop, solving this problem involves becoming familiar with the zonal statistics tool.

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You can achieve this using the v.rast.stats module in GRASS GIS

There is also a faster version of it on the GRASS AddOns page

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