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I am doing some mapping that requires country and region average coordinates.

I've found this very useful table with the coordinates of countries, their ISO 3166-1 alpha-2 code and the average coordinates of each. However, this list does not include regions.

Is there a similar source that includes countries and regions?

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    If this is open data then the place to ask may be the Open Data Stack Exchange. – PolyGeo Dec 29 '18 at 3:07
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This is a somewhat complicated request because there is significant variation in what a "country" means. For example, ISO 3166-1 treats Puerto Rico as part of the USA, but the US (via its profile, called GENC) treats it as a separate top level entity. There are more complications in terms of disputed areas (e.g. Taiwan, Arctic Ocean, Kashmir). It also depends a bit on your needs (e.g. do you only care about land areas, or do you want to include maritime boundaries, which are again complicated in terms of Archipelagic States).

I'd suggest starting with some of the options available from Natural Earth - perhaps https://www.naturalearthdata.com/downloads/10m-cultural-vectors/ might be a good starting point. Otherwise you may be able to refine some of that data to meet your needs using QGIS or similar software and some buffer / union operations.

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