A small dataset is represented by the values $\{x_1, x_2, x_3, x_4\}$. If the sum of these values is $\sum x_i = 40$, and the sum of their squares is $\sum x_i^2 = 450$, what is the sum of the squared deviations from the mean, $\sum (x_i - \bar{x})^2$?