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I bought xperia zr last week. It was showing 3+GB free memory. There were some videos (demo, movies trailers, music) which came when i got the mobile. They were occuping around 1GB of space. To get more free memory i deleted all of them. After doing this i again checked the free memory. But still i am getting same amount of free momory. Just for confirmation i checked again if videos are still there but didnt find them.
One more point. I installed only 2-3 apps which were of very small size. Didnt even installed any game.
part of th einternal storage its only for apps, another part for pictures, music, videos, download files, bluetooth, etc. and the third memory will be an SD card.
go to settings > storage and post a screenshot