Given a dataset where the mean is $\mu$ and the variance is $\sigma^2$, consider the effect of a nonlinear transformation $y = x^2$. If the original dataset is $X = \{-2, -1, 0, 1, 2\}$, how does the mean of the transformed set $Y = \{x_i^2\}$ compare to the square of the original mean $\mu^2$?