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I moved from QGIS 2 to QGIS 3 I cannot seem to be able to use the zonal statistics package.

Basically what I want to do is take the world pop GeoTIFF for a country and then calculate the population based on a shapefile/polygon. I was able to do that easily in QGIS 2 but the package seems to be missing in QGIS 3. Any hints?

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Zonal statistics for raster layers can be found in the processing toolbox:

https://docs.qgis.org/3.10/en/docs/user_manual/processing_algs/qgis/rasteranalysis.html?highlight=zonal%20statistics#raster-layer-zonal-statistics

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Open the 'Processing Toolbox' via Processing > Toolbox and search for "Zonal Statistics"

example

Additionally to the option suggest by @babel, there are two more options, respectively

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