480 'Journal of Comparative Neurology and Psychology. 

 MEAN, STANDARD DEVIATION, AND COEFFICIENTS OF VARIATION. 



I (F. f) 

 In the equation J = , where A represents the mean, 



it will be clearly seen that the absolute value of mean (A) varies 

 directly according to the greater or smaller number of frequencies 

 associated with the smaller or greater values of F, as long as " n," 

 the total number of variates, is constant. We have demonstrated 

 above that the number of the observed frequencies of F for both 

 cells and their nuclei cannot be considered as the true frequency 

 owing to the method of section. The true frequencies for the 

 smaller values of F should be the observed frequency minus those 

 cells which have been transferred from the group of large cells, 

 while for the larger values of F it should be observed frequency 

 plus those cells which have been thus transferred. Consequently 

 the mean values actually found for the cell-bodies and nuclei must 

 be considered as smallerthan they should actually be. However we 

 cannot determine at the present moment how large the true mean 

 values should be, owing to the difficulty of determining the number 

 of the cells and nuclei which are assumed to have been transferred. 

 On the other hand, the values for the standard deviation and for 

 the coefficients of variation in the present case should be smaller 

 than those found, since following an increase in the frequencies 

 towards the larger values of F the resulting frequency distribution 

 would become more regular than they are shown to be by the ob- 

 served polygons and consequently the mean square deviation would 

 become smaller. Diminution in the mean square deviation causes 

 a reduction in the value of the standard deviation and conse- 

 quently in the value of the coefficients of variation. As a matter 

 of fact, we found the value for the standard deviation as well as 

 the coefficients of variation decidedly larger when compared with 

 apparently more variable characters. For example Pearl ('05) 

 found the coefficient of variation in Paramecium from 8 to 

 9 per cent and in Arcella 10 per cent (Pearl and Dunbar, '03) 

 while in the present case that of the cell-body is as high as 28 per 

 cent and that of the nucleus 17 per cent. Although we have not 

 as yet any available data with which directly to compare our own, 

 nevertheless our own values appear too great when they are 

 compared with the coefficients of variation obtained from the 

 measurement of highly variable organs like the weight of the 



