Xcode 7.1.1 opens up as Xcode 7.0.1
If you are tired downloading Xcode from the App Store or searching for old Xcode.apps somewhere hidden on your volumes, go to Developer Apple Downloads, enter a valid Apple ID and password and download Xcode 7.1.1.dmg (direct link) and any other tool you need to code or debug.

Remove any Xcode.app in your /Applications folder, open the dmg and copy Xcode to your /Applications folder.