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I see maps with all kind of statistics (gdp, population density, rain, exports, happiness) on the internet all the time. Usually they're only outlines (so they have no roads or buildings or whatever) because what matters is the colour indicating the presented statistic's level.

I can draw something like that, of course, but I can't believe all those people are doing it by hand. They have data sources, they have blank vector(?) maps, and they surely must use some software that connects the two using a chosen type of presentation (colours, etc). But this is something I've found it very hard to web search for, because the keywords I can think of are too generic. I've found links to GIS software but no explanation of how it can be used to connect data to maps, nor where to find the maps themselves (surely folks aren't drawing them and the country/region/council borders by hand). I don't even know if GIS software is what people use for the purpose (it looks both overkill and low-level to me).

Can anyone provide me with some specific information?

edit: this isn't, as reported, a question 'seeking product, service, or learning material recommendations' that 'become outdated quickly and attract opinion-based answers'. Instead, it's a description of the 'situation and the specific problem' as indicated: I'm not asking for recommendations, I'm asking how this kind of problem is generally solved.

There is an answer below that does exemplify how the problem is solved with recourse to a specific product, but that's beside the point.

edit: I've since found a similar, but more specific, question Creating map of countries colored using country statistics. For some reason it didn't show up in my original queries. It focuses on tools for 'map charting' - it appears to corroborate that that's the name of the field.

entonio
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Creating map chart is really a basic capacility now, even Excel can do it

If you're interested in more, just Google for "map chart" and your favourite tool's name.

Many of the tools has their own embedded maps, if you need more, the most wildly used format is ESRI shapefile.