The install.sh Linux script included in the latest release doesn't appear to actually install anything, other than some unnecessary desktop icons. Ideally, this should install the Arduino IDE itself into the proper location.

Assuming you extract the tarball into ~/arduino-1.8.1, installing should at minimum do:

sudo mv ~/arduino-1.8.1 /usr/share/arduino
sudo ln -s /usr/share/arduino/arduino /usr/local/bin/

This is the location the current Ubuntu Arduino package uses (although it's Arduino IDE version is ancient), and allows all users easy access to the IDE without worrying about setting up their PATH or other user session variables.