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I have a data table that I need to trim down, merging records which have the same value in an ID field and performing a couple math operations on various other fields (summing, averaging). The Dissolve tool in ArcGIS does this for feature classes, but it doesn't work on tables. I realize there's probably a tool in ArcGIS that does this (it's basically a Dissolve with no geometry) but I haven't found it and am in a bit of a hurry.

Is there one? I have an ArcInfo license available if necessary.

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You can do this with the Summary Statistics (Analysis) tool. The case field parameter is what you use to "dissolve". From the above link:

case_field [case_field,...] (Optional) The fields in the Input Table used to calculate statistics separately for each unique attribute value (or combination of attribute values when multiple fields are specified).

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    This answer is correct for the specific question; however, I want to provide a warning to those who may be looking to dissolve without any statistics fields: it won't work. You must submit a statistics field. If you're looking to "dissolve" a table but not calculate summary statistics, then you can use the Delete Identical tool. desktop.arcgis.com/en/arcmap/10.3/tools/data-management-toolbox/… – Tom Jul 12 '16 at 16:58
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This sounds like you need to look at the Summary Statistics tool which I find to be a bit of a Swiss Army Knife in that it comes with a Basic (formerly called) ArcView level license and can often be used in place of Frequency (that needs Advanced/ArcInfo) and PULLITEMS (that needs ArcInfo Workstation:-) to reorder fields.

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The Dissolve_management tool works on tables as well as feature classes.

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    ? In arcgis desktop 10.3.1 I get an "One or more dropped items were invalid and will not be added to the control." error. (ArcToolbox >> Data Management Tools >> Generalization >> Dissolve) – matt wilkie Dec 10 '15 at 18:37

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