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I want to make population density map for EU where I can show populations of people aged about 65yrs, where can I get a EU shapefile and population Excel file?

Is there any EU shape file available with country boundaries or will I have to create one myself by collecting each country of EU? I have downloaded NUTS 2013 but its attributes hard to understand.

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From Eurostat database, you can find:

Population density by NUTS 3 region (demo_r_d3dens)

The data in TSV format can be retrieved from this link. For excel, format, use this tool to filter the dimension you need and retrieve it as XLS format with the download button. The corresponding NUTS geometries can be downloaded (here). To make a chloropleth map, you need to perform a join, for example with QGIS. Otherwise, here is an example of how to do that quickly with Eurostat_map.js tool.

Otherwise, for finer spatial analyses, you can get the total population figures over Europe on a 1km resolution grid from Eurostat-GISCO website, for years 2006 and 2011. For more information on how this was produced, see GEOSTAT 1 project. For a breakdown by age group with this spatial granularity, you have unfortunatelly to wait for some more years, until the census 2021 regulation is implemented.

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