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ArcGIS has a few nifty table tools, including Summarize and Statistics. Is there a way to access them through arcpy, or will I have to hack my own methods via math and lists?

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You appear to be referring to Summary Statistics which :

Calculates summary statistics for field(s) in a table.

If you are looking for other statistical values not available through the conventional interface, for numeric fields, then you could have a look at:

http://resources.arcgis.com/gallery/file/geoprocessing/details?entryID=BDF21676-1422-2418-34E6-A29C6BAC8A0B

A variety of statistical parameters, including several instantiations of skewness and kurtosis, can be derived as well as the ability to obtain frequency distributions for said data.

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