Now a days a Mac should have Administrator and a password.
The first account you created when you set up the computer for the
first time is an Administrator account
Password should not be blank.
Apple demands it.
You might have turned on "Automatic Login" in System Preferences > Users & Groups > Login Options.
You can keep doing it if you upgrade the OS X to Mavericks.
Hope you remember the Administrator name and password.
To install Mavericks, you have enter Administrator name and password to authenticate.