Updating iTunes from version 9.0.3

I have recently updated my 2007 Macbook to OS X 10.6.8, and have been updating my software, but remain unable to update iTunes. I have downloaded, and run the installer, and it says the says the software has been successfully installed, but when I open iTunes, it is still the old version. Do I need to uninstall the old version before updating? I didn't think this was necessary, so I am confused.

Any help is greatly appreciated!

Thank you.