I have downloaded an app (its a game), made some test progress, and then deleted the game data. I have also cleared the cache and uninstalled the game, but whenever I install it again from the Google Play Store, the progress is still there.
I have also tried installing the app after clearing its data, offline from the .apk-file.
How is it possible to retain the app data like this and how can I clear the data?
Since you mentioned you were still seeing it after installing offline, I'm going to assume you also tried the game while still offline. If the data was there, it could have made a folder to hold the data which you could get to and delete using a file explorer. There's a number of apps that make folders to hold data that don't get deleted when the app is uninstalled.
It's possible that the game progress is saved in the cloud, if you are using Google Play Games.
The Google help page says you can clear this progress / data, but note that it will clear for ALL games:
If you want to delete your saved data from all games that use Cloud Save, visit the Google Settings app and select Menu > Clear app data. This will clear all your data from all accounts.
Depending on your device, your Menu icon may look different.
