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Instructions provided describe how to get more accurate results from the Zonal Statistics function. Running the Zonal Statistics Spatial Analyst function with features as the zones gives a result that overestimates the number of cells that fall within a polygon. This is because features are converted to raster as part of the processing. Cells that only partially fall within the boundary of a certain feature are included if the cell is encountered first in the conversion processing.
To verify that the result does not overestimate the number of cells that fall within each polygon, convert features to raster in Workstation GRID and use the result from this as the zone dataset in the Zonal Statistics function.
At the GRID prompt, cells are included if the majority of the cell is contained within the feature's boundary.