The linear ordering theorem for weighted means of functions relative to weight functions (Glaser, 2001) has several interesting implications similar to those of the one dimensional Cashwell - Everett mean (Cashwell - Everett, 1969). As an immediate consequence of the linear ordering theorem, we develop in this article the n- dimenstional deviation theorem and a theorem dealing with inequalities related to the magnitudes of the defining functions of the n-dimensional means. [corrected version 1/2003]