If you've picked an existing partition to install a new OS on, then it will have overwritten that partition & put all it's own files there. This means that the partition has been, in effect, removed & replaced, and formatted, and data written to it.
The old partition most likely had data stored toward the beginning of it; depending on your luck, historical usage, and amount of space used, it is possible that some data might have survived even this treatment! If there wasn't much prior use of the drive then you're likely out of luck by now.
The odds of getting much back are thin; however, if there was important stuff there, you could try the following:
Reboot from a live system, ie CD or USB.
Download a forensic tool such as testdisk, or foremost - I use foremost, and the other question referenced above, used testdisk, so I'll talk about foremost:
Run this, using a partition other than the target to store found data - an external drive is good - with the target as your old 'F' drive.
Type in foremost -o /path_to_destination_storage -i /dev/sda4
, replacing sda4 with the correct designation for your old 'F' drive.
This will produce a mess of randomly named files, classed by type, representing the files it found and recognised including the "blank" parts of the drive which not not be as blank as expected!
You can then set about playing found media, viewing pictures, searching text files, to see if you got anything back.