40 



SUMMARIZATION OF DATA 



Ch. 2 



1.00 



Figure 2.61. 



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 2.61. 



2.7 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 0.06, 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 16%. 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 2.13, ax = 



2j2 



(2X) 2 /N 



N 



is the standard deviation of X. For the measurement, kX, 



VkX = 



N 



2(kX) 2 - (XkX) 2 /N fc 2 2X 2 - k 2 -{?X) 2 /N 



N 



= k- 



(TX- 



