Given a dataset $X$ with $n=100$ observations, the third central moment is defined as $\mu_3 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^3$. If $\sum x_i^3 = 50000$, $\sum x_i^2 = 1000$, $\sum x_i = 100$, and $\bar{x} = 1$, what is the value of $\mu_3$?