The "Cyclic Redundancy Check", or CRC, is a small value generated from a file's complete contents. They typically get stored with compressed files and installers to make sure that the final installed files are identical to the original source files packed into the installer. (zip files use these too)
This means that CRC errors like the one you got are generally a sign of actual physical damage to the data. Are there any scratches on your game disk?
Note that these errors occasionally occur in situations where an installer doesn't have administrator rights, so that could be a possible cause as well.
If you really don't manage to install the game from your DVD, you can always make an Origin account and install the Origin application (if you don't have those already) and add the game to your Origin library. To do that, open the "Origin" menu in the Origin client program and select "Add Game". Then, choose "Redeem Product Code" and enter your game serial. The product should be added to your Origin library, from which you can install it by downloading it through the application.