In this video I demonstrate a workflow of how you can calculate the population for any area in the world using global raster population data from WorldPop. In the example we do this for an area of Mexico but you can find data for your own country - or the entire world - and replicate it very easily. If you already have your own shape then you don't even need to do the vector layer creation bit included here.
Data: www.worldpop.org/datacatalog/
NASA SEDAC population estimator: sedac.ciesin.columbia.edu/map...
See my intro and intermediate QGIS courses for more: www.udemy.com/user/alasdair-r...