At a local high school, the basketball coach measured the height of each player. Nine of the ten heights, in cm, were \(180\), \(181\), \(183\), \(187\), \(188\), \(190\), \(193\), \(195\), and \(196\). The height of the tenth player, Richard, was a whole number.
Initially, the coach measured Richard’s height incorrectly. After the error was corrected, both the mean and median of the heights increased by \(0.5\) cm.
Determine all the possible values for the height of Richard.