380 EXAMPLES OF CHEMICAL CORRELATION 



successive births of very varying size in proportion to the bodily dimen- 

 sions of the mother. The moment of delivery is, in fact,. primarily 

 determined by physiological factors in the mother, rather than by the 

 stage of development of the fetus at term. This may be very clearly 

 seen by comparing the Variability of the duration of gestation with 

 the variability of the weights of the infants which are delivered. 



The ordinary method of measuring the variability of any quantity 

 which is adopted by statisticians consists in expressing it in terms of the 

 percentage ratio of the Standard Deviation of the quantity measured to 

 its average value. The standard deviation is the square root of the 

 mean square of the observed deviations from the average. Thus, 

 consider the following illustrative sets of measurements. 



i 11 101 



2 12 102 



3 13 103 



4 14 104 



5 15 105 



It is obvious at a glance that the figures in the first column are very 

 variable, those in the second column moderately so, and those in the 

 third volumn relatively invariable or approximately constant. When 

 we wish to express this impression in arithmetical terms we proceed as 

 follows : 



Average of the first Average of the second Average of the third 



column. column. column. 



3 . 13 103 



the deviations from the average are in each case 2, 1, 0, 1 and 2. The 

 sum of the squares of these deviations is 4+1+0+1+4=10. The 

 mean square is therefore 2 and its square-root, which is the standard 

 deviation, is 1.414. The variability of each of the columns of figures 

 is the ratio of this quantity to the average, expressed as a percentage, 

 which works out as follows: 



Variability of first Variability of second Variability of third 



column. column. column. 



47. 1 per cent. 10.9 per cent. 1 . 37 per cent. 



Our impression of the relative variability of the three columns of 

 figures is thus expressed in quantitative terms, the actual meaning of 

 the results being, that in the first set of figures two-thirds 1 of the 

 recorded values will be found to differ by less than 47.1 per cent, from 

 the mean, in the second set two-thirds of the recorded values will differ 

 from the mean by less than 10.9 per cent, of its value, and in the third 

 set of recorded values two-thirds will fall within 1.37 per cent, of the 

 mean. 



Applying this method to the study of the comparative variabilities 

 of the period of gestation and of the weights of the infants delivered 

 thereafter, we find that the two variabilities bear no proportion to 



1 Or, more precisely, 68.27 per cent. 



