A dataset is formed by pooling three groups: Group 1 ($n_1=10, \bar{x}_1=5, s_1^2=2$), Group 2 ($n_2=10, \bar{x}_2=10, s_2^2=2$), and Group 3 ($n_3=20, \bar{x}_3=15, s_3^2=3$). What is the population variance of the combined dataset of $40$ observations?