The correct answer is $\boxed{\text{C) 36}}$.
The variance is a measure of how spread out a set of numbers is. It is calculated by taking the square of the distance from each number to the mean. In this problem, the mean is 12. The distances from each number to the mean are 0, 3, 6, 9, and 12. The squares of these distances are 0, 9, 36, 81, and 144. The variance is therefore $\frac{0 + 9 + 36 + 81 + 144}{5} = \boxed{36}$.
Option A is incorrect because it is the square of the standard deviation. The standard deviation is a measure of how spread out a set of numbers is, but it is not the same as the variance.
Option B is incorrect because it is the square of the mean. The mean is the average of a set of numbers, but it is not the same as the variance.
Option D is incorrect because it is the square of the median. The median is the middle number in a set of numbers, but it is not the same as the variance.