A Measure of Dispersion for Ordered Series

Abstract

A statistical series may be assigned to one of two broad classes according as it consists merely of a list of numbers of indefinite arrangement, or has its items ordered relative to a particular variable. Typical of the first class are the series composed of experimental measurements, and chief illustrations of the second class are to be found in historical series in the field of economic statistics. The common statistical coefficients have been developed in the study of, and are peculiarly applicable to, series of the first class; and i t is a question of considerable moment whether such coefficients are equally useful in the analysis of an ordered series of the second class. The chief measure of dispersion is the standard deviation, the square root of the mean squared deviation from the arithmetic mean. It is apparent from the method of calculation of the standard deviation that it can take no account of the arrangement of the variates. Example (i). Consider the two series (a) 3 7 4 6 2 5 8 7 3 4 7 3 5 8 2 6 (b) 2 3 2 3 4 5 5 6 7 7 8 7 8 6 3 4