OK, I was hoping to avoid the big answer.
You need to create the default database files. The command to do this mysql_install_db.
If you are planning to run mysql as mysql user, which is what you must do, for security reasons,
if the is no mysql user/group do as root
useradd -g mysql mysql
and then log in as mysql like this:
as root do
and type the above command (mysql_install_db).
Hope it helps