excess means a tendency to make the frequency curve topheavy around 

 the mean; a negative excess indicates a flattening tendency. Once 

 having computed the various statistical parameters represented by the 

 mean, the dispersion, the skewness and the excess, the frequency distri- 

 bution is easily ascertained for any value of the varying attributes and 

 reduced to a common standard of measure. This method has been 

 followed and is sufficiently explained in the diagrams of frequency 

 distribution of the conscripts of Norway, Sweden, Denmark, Wurttem- 

 berg and Japan, and the corresponding measurements of recruits of 

 the United States Army previously to the present war. (See diagram 

 on page 32.) All of the frequency dispersions have been reduced 

 to English measure. The values of the various statistical parameters 

 are as follows : * 



STATISTICAL AND MATHEMATICAL CONSIDERATIONS OF 



FREQUENCY DISTRIBUTION IN PHYSICAL 



PROPORTIONS 



COMPARATIVE MEASUREMENTS 

 Values of the Various Statistical Parameters 



According to this table the variation is most pronounced in the 

 case of the Danes. The Swedes are evidently the tallest of the races 

 included in the comparison, showing both a positive skewness and a 

 positive excess. Computing the distribution from the equations of 

 the frequency curves, Mr. Fisher presents the following comparative 

 results on the basis of 1,000 standard measurement^ progressing by 

 one-inch intervals for the six countries for which the data could be 

 secured. 



* For an elementary description of frequency distributions see "Elderton's 'Primer of 

 Statistics'" (London, 1910), and H. Secrist's "Introduction to Statistical Methods" (New 

 York, 1917). A more advanced treatment is to be found in Udny Yule's "Theory of Sta- 

 tistics" (London, 1911). Of special value are the observations by Secrist on the Graphic 

 Presentation of Simple Frequency Series. He properly directs attention to the common 

 error of "Taking measurements with extreme accuracy and then grouping them into broad 

 classes." And he suggests that "Measurements should be so grouped as to show the 

 variability and at the same time to leave the frequency distribution fairly smooth." "For," 

 he remarks in continuation, "in the matter of grouping there are two opposing tendencies 

 — grouping into too few classes to show variability and grouping into too many classes to 

 give a smooth distribution." In many cases "the law of distribution is hidden because of 

 too much detail." 



31 



