On Grouping for Maximum Homogeneity

Abstract

Abstract Given a set of arbitrary numbers, what is a practical procedure for grouping them so that the variance within groups is minimized? An answer to this question, including a description of an automatic computer program, is given for problems up to the size where 200 numbers are to be placed in 10 groups. Two basic types of problem are discussed and illustrated. * This paper is the result of work supported by the Social Science Research Council and by the Bureau of General Research of Kansas State College; also by the courtesies extended to the author by the University of Illinois when he visited there during the summer of 1956. The author gratefully acknowledges the helpful suggestions he received from W. A. Neiswanger, Kern Dickman, and D. B. Gillies of the University of Illinois; from J. I. Northam, now with the Upjohn Company; and from Henry Tucker, now of the University of Arizona. Notes * This paper is the result of work supported by the Social Science Research Council and by the Bureau of General Research of Kansas State College; also by the courtesies extended to the author by the University of Illinois when he visited there during the summer of 1956. The author gratefully acknowledges the helpful suggestions he received from W. A. Neiswanger, Kern Dickman, and D. B. Gillies of the University of Illinois; from J. I. Northam, now with the Upjohn Company; and from Henry Tucker, now of the University of Arizona.