328 



Variation and Correlation in Aredia 



in the two cases aro diftorcnt. If we comparc, instcad of thc absolute, the relative 

 tlifturences, by taking the percentages of the differeuces betwcen mean aud mode 

 in the respective means, wo reach thc following results : the percentage difference 

 between the mean outer diameter and the modal outer diameter in the niean 

 outer diameter is 5-78 °/„. The percentage difference bctwccn the mean inner 

 diameter and the modal inner diameter in the mean inner diamcler is 5"49 °/„. 

 These relative values are in closc accord and Icad to tlic same conclusion regarding 

 the relative skewness of the two curvcs an that reached by merc inspcction, namcly, 

 that tbe two distributions are very closely alike in their form. We would suggest 

 this method just described of taking the percentage difference between the mean 

 and the mode as a useful rough method of comparing the relative skewness of 

 frequency distributions, in cases whcre it is not feasible to conipute the skewness 

 exactly from the moments*. 



From the mean values for the two diamcters it is seen that the whole diameter 

 of the shell (outer) is on the average approximately 3'5 times the diameter of the 

 " mouth " opening (inner). More exact relations between these two dimensions will 

 be given later in the paper in the form of regression equations. 



The coeflficients of Variation show clearly that the inner diameter is distinctly 

 more variable than the outer. This rclation is shown in Table IV. 



TABLE IV. 

 Coefficients of Variation. Outer and Inner Diameters. 



Thc difference is roughly ten times its probable error and hcnce may be con- 

 sidcrod significant. 



These two frequency distributions furnish a good cxample of a case whcre the 

 absolute conccntration of variates given by the Standard dcviation cannot bc uscd 

 for the comparison of the relative variabilit}' of two characters in which the 

 means are widely different. According to thc Standard deviations in the case 

 under consideration the outcr diameter would appear to be twice iis variable as 



[* Skewness has been defined as the ratio of the distance between mean and mode to the standard- 

 deviation ; we find for it in tlic above cases : -5032 for outer, -4027 for inner diameter distribntions. 

 These aro considerable amounts and readily comparablu with tbe values found in othcr cases. Ed.] 



