Suppose it is desired to partition a distribution into k groups (classes) using squared error or absolute error as the measure of information retained. An algorithm to obtain the optimal boundaries (or class probabilities) is given. For the case of squared error optimal class probabilites were obtained for k = 2 to 15 for beta (for various values of the parameters), chi-square (12 d.f.), exponential, normal, and uniform distributions. Results obtained are compared and analyzed in light of existing papers. Special attention is given to the case k = 5, corresponding to the assignment of the letter grades A, B, C, D, F in courses, and to the case k = 9, corresponding to stanines.