ls -l /var | grep lib; ls -l /var/lib | grep mysql
drwxr-xr-x   13 root     root         4096 Jan 25 20:44 lib
drwxr-xr-x    4 mysql    mysql        4096 Jan 25 22:40 mysql
================

here is what I have in /etc/my.cnf

[mysqld]
datadir=/var/lib/mysql
socket=/var/lib/mysql/mysql.sock

[mysql.server]
user=mysql
basedir=/var/lib

[safe_mysqld]
err-log=/var/log/mysqld.log
pid-file=/var/run/mysqld/mysqld.pid