A New Measure of Dispersion

The measures of dispersion in common use are: (1) the standard deviation; (2) average deviation; (3) quartile deviation; and (4) the range. It is generally admitted that the merit of the range as a meas? ure of dispersion lies in its simplicity of determination and interpre? tation. To calculate its probable error has not been attempted; but were this done it would have little significance, for the range itself is not a constant function of a distribution, since, in general, it increases with an increase in population. The range is therefore unsatisfactory as a measure of dispersion, because it undoubtedly has a large probable error, and also because its significance varies as populations of different sizes are being considered. The probable errors of the other three measures are given in the sec? ond column of the accompanying table. The values in columns 2 and 3 must be multiplied by the standard deviation of the distribution, and the values in columns 2_and 4 must be divided by the square root of the number of cases (Vn) before they will serve in any particular prob? lem. For purposes of comparison of different measures, these factors are here omitted.