l\Q Pearl and Surface. 



with the random sample of plants of this variety (series F) in respect 

 to final height. But as clearly shown by the curves, the plants of 

 series D began to mature much earlier than those of the other series. 



Changes in the Standard Deviation. 



Tables 1 — 6 give the stauclai»d deviations and the coefficients of 

 variation for the different dates and for each series. Fig. 2 shows the 

 standard deviations for all six series. The standard deviation is a 

 measure of the absolute dispersion, and in cases like the present where 

 the mean is changing so rapidly, it cannot be taken as a good measure 

 for comparing the variability of the successive growth stages. Still, 

 certain points of interest can be brought out by a study of these constants. 



From Fig. 2 we note that there is a gradual increase in the 

 standard deviation in the early portion of the curves. From about 

 July 1 to 15 there is a marked increase in the size of this constant. 

 This increase is undoubtedly associated with the tasseling of the plants. 

 Those plants on which the tassels appear first, grow faster and in this 

 way increase the dispersion of the individuals. After the middle of July 

 all tassels have appeared and the individuals become less scattered about 

 their means. 



In the above discussion it should be remembered that the rapid 

 increase in the size of the standard deviation is associated with a rapid 

 increase in the mean of the observations. In general the larger the 

 size of the thing measured the larger its absolute variability will be. 

 The changes in the relative variability at this period will l)e shown in 

 the discussion of the coefficients of variation. 



Changes in the Coefficient of Variation. 



The changes in the coefficients of variation for the successive 

 measurements and for all six series are displayed graphically in Fig. 3. 

 It will be noted that on the whole the relative variability decreases 

 and is, on the average, about ten percent lower in the matured plants 

 than at the beginning of the season. Such a decrease in the relative 

 variability is characteristic of growth curves. This is shown in the 

 statistics of the growth of children (vide infra p. 114). MiNOT ('91) 

 first discussed it in connection with the growth of guinea pigs and 

 Pearl ('07) has developed the same idea in the case of intraindividual 

 growth of the leaf whorls on Ceratophyllum. This law of diminishing 

 variability appears to be of fundamental significance. 



