INTRODUCTION 29 



In this particular case the doubling of the intervals for the groups 

 does not smooth out the drop near the right-hand end of the curve, but 

 the entire curve becomes otherwise more symmetiical. The other way to 

 smooth out an irregular curve is to increase the number of instances, 

 measure another hundred, for instance, which would tend, by the doctrine 

 of chances, to fill out the short columns. 



One of the main uses of frequency curves is to show the general 

 distribution of a certain set of measures or other statistics. The highest 

 point in the curve marks the point of greatest frequency, the one that 

 has the most votes, so to speak, and is called the mode. In the measure- 

 ment of the same parts in two distinct human races, it may often happen 

 that the modes of the two races differ from each other, which would be 

 well brought out by superposing one curve upon the other. A bi-modal 

 curve, or one with two crests, is sometimes found to be the result of the 

 use of mixed material, that is, in anthropology, from the mixture of two 

 differently proportioned races; and while this does not always prove to 

 be the cause, such a curve always leads the anthropologist to suspect 

 that such may be the case. 



III. The Arithmetical Mean 



This is what is usually referred to as the average, and is one of the 

 first things to be ascertained from the usual results of the measurement 

 of a certain length in a number of individuals. The most simple method 

 of obtaining it is by actual summation, i.e., adding the several results 

 together, and dividing by the number of instances (individuals). Thus, 

 in the following measurements of the cristal breadth (between the hips) 

 of the same 100 students that furnished the radius length measurements, 

 the arithmetical mean is calculated by actual summation : 



Total value 



205 



215 



225 



235 



1,960 



3,825 



5,300 



4,950 



4,845 



4,130 



915 



315 



100 27,120 



27,120 -r- 100 = 271.2, the arithmetic mean. 



In this case it will be noticed that the value taken for each group is 

 the mid-value between the two extremes of the group. There is still 



