It's quieter AND uses a crap load of space.
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When the Xbox says install game it does not mean you are about to install the full game onto your hard drive. When you install a game on to your Xbox it's taking some of the game files and installing them to make the game run smoother and possibly look better.
It basically cuts the loading time on the game etc...
In the hardrive in the console.
Installing an Xbox 360 to your HDD improves loading times, removes disc noise and overall creates a smoother gaming experience. But you still need the disc in the Xbox 360 Console to play the game.
you should always be able to play online without installing a game