Elements of statistics (1954) Elements of statistics elementsofstatis00frye Year: 1954 40 SUMMARIZATION OF DATA Ch. 2 Figure 60 70 80 90 100 110 120 130 140 Birth weight in grams Graph of the relative cumulative frequency distribution for the data of Table THE COEFFICIENT OF VARIATION There is considerable need for a measure of relative variability in one set of numbers as compared with another when the units of meas- ure, or the levels of magnitude of measurement, are quite different. The standard deviation, the mean deviation, and the range are ex- pressed in the sam
Elements of statistics (1954) Elements of statistics elementsofstatis00frye Year: 1954 40 SUMMARIZATION OF DATA Ch. 2 Figure 60 70 80 90 100 110 120 130 140 Birth weight in grams Graph of the relative cumulative frequency distribution for the data of Table THE COEFFICIENT OF VARIATION There is considerable need for a measure of relative variability in one set of numbers as compared with another when the units of meas- ure, or the levels of magnitude of measurement, are quite different. The standard deviation, the mean deviation, and the range are ex- pressed in the same units as those in which the data were taken; so they obviously reflect the general size of those units. Suppose that one bushel of a particular sort of crop weighs 60 pounds, on the average. Then the frequently used unit 'pounds per 1/1000 acre' is but , or 6 per cent, of the size of the unit 'bushels per acre.' Hence to convert yields in pounds per 1/1000 acre into bushels per acre would require multiplication by 163^. To see what effect such a procedure has on the standard deviation, consider the general case of two measurements X and kX, where the k is any con- stant. For example, X could be the number of pounds per 1/1000 acre so that k = 16%%%%%%%%%%%%%%%%. By formula , ax = vy2 {^Xf/N N is the standard deviation of X. For the measurement, kX, (TkX = N 2(fcX)2 - (XkX)yN k^i:X^ - A;2.(2X)ViV N = k- o-x-
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