THE MEASUREMENT OF VARIATION. 29 



method of estimating variability, however, the plan is 

 sometimes adopted of determining this index, and then 

 reducing it to terms of probable error by multiplying 

 by .6745. Similarly an arithmetic mean error may 

 be reduced to terms of probable error by multiplying by 

 .8453. 



It will have been noticed that in the series of meas- 

 urements from time to time referred to, a few excep- 

 tions to the general law of distribution of variations 

 were mentioned. In these cases the variations were 

 not distributed evenly about the middle ordinate, but 

 the curve of distribution was asymmetrical, or skew. 

 Such series as these are by no means uncommon, espe- 

 cially in the case of plant statistics. For instance, De 

 Vries * found that the number of petals in the butter- 

 cup varied between 5 and 10, the frequency of distribu- 

 tion being as follows: 



Number of petals, 5 6 789 10 11 



Frequency observed, 133 55 23 7 2 20 

 Theory, 136.9 48.5 22.6 9.6 3.4 .8 .2 



Here flowers with the smallest number of petals occur 

 the most, and those with the largest number the least, 

 frequently. The values marked " Theory ' in this 

 and the next series will be referred to later. 



Again De Yries cultivated a variety of clover in which 

 the axis is very frequently prolonged beyond the head 

 of the flower, and bears from one to ten blossoms. The 

 following were the frequencies of occurrence of flowers 

 with none of these blossoms, or with various numbers 

 of them : 



*Ber. d. deutschen bot. Gesellschaft, xii. p. 203, 1894. 



