The paper presents inequalities between four descriptive statistics that can be expressed in the form [P-E(P)]/[1-E(P)], where P is the observed proportion of agreement of a "kappa x kappa" table with identical categories, and E(P) is a function of the marginal probabilities. Scott's "pi" is an upper bound of Goodman and Kruskal's "lambda" and a lower bound of both Bennett et al. "S" and Cohen's "kappa." We introduce a concept for the marginal probabilities of the "kappa x kappa" table called weak marginal symmetry. Using the rearrangement inequality, it is shown that Bennett et al. "S" is an upper bound of Cohen's "kappa" if the "kappa x kappa" table is weakly marginal symmetric. (Contains 3 tables.)