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I am trying to analyze the number of schools per square kilometer in Madagascar, but only considering the number over inhabited areas. I have data on schools from the World Bank, but I can't find a reliable source of data for populated areas.

I have looked at the data on Open Street Maps but the extent and quality of the data varies a lot by sub-region. Some areas have many buildings and roads mapped while others do not. I lived in Madagascar for four years and I can tell that these gaps are due to missing data. I joined select land uses with a buffer around buildings to get an "inhabited areas" layer, but the measure of schools per area is also varying unrealistically (some places have more than 50 up to thousands of schools per square kilometer of calculated area).

Where can I find data on inhabited/populated areas to compliment or replace OSM? Are there any strategies this community has come across for finding or calculating measures of populated areas?

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You can get all sorts of gridded population data (e.g. counts or density) from the Worldpop website, this includes Madagascar. Methodology is discussed here.

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