iQ STATISTICAL METHODS. 



CHAPTER II. 



ON THE SERIATION AND PLOTTING OF DATA AND THE 

 FREQUENCY POLYGON. 



The data obtained by measuring any character in a lot of 

 individuals consists either of amass of numbers for the charac- 

 ter in each individual ; or, perhaps, two numbers which are to 

 be united to form a ratio ; or, finally, a series of numbers such 

 as are obtained by the color wheel, of the order : W 40$, N 

 (Black) 38$, 7 12$, O 101 The first operation is the simplifi- 

 cation of data. Each variate must be represented by one 

 number only. Consequently, quotients of ratios must be de- 

 termined and that single color of a series of colors which shows 

 most variability in the species must be selected, e.g.,N. 



The process of seriation, which comes next, consists of the 

 grouping of similar magnitudes into the same magnitude 

 class. The classes being arranged in order of magnitude, 

 the number of variates occurring in each class is determined. 

 The number of variates in the class determines the frequency 

 of the class. Each class has a central value, an inner and an 

 outer limiting value, and a certain range of values. 



The method of seriation may be illustrated by two examples ; one of 

 integral variates, and the other of graduated variates. 



Example 1. The magnitude of 21 integral variates are found to be as 

 follows : 12, 14, 11, 13, 12, 12, 14, 13, 12, 11, 12, 12, 11, 12, 10, 11, 12, 13, 13, 

 13, 12, 12. In seriation they are arranged as follows : 

 Classes: 10,11,12,13,14. 

 Frequency : 1, 4, 11, 4, 2. 



Example 2. In the more frequent case of graduated variates our mag- 

 nitudes might be more as follows : 



3.2 4.5 5.2 5.6 6.0 . 

 3.8 4.7 5.2 5.7 6.2 

 4.1 4.9 5.3 5.8 6.4 



4.3 5.0 5.3 5.8 6.7 

 4.3 5.1 5.4 5.9 7.3 



In this case it is clear that our magnitudes are not exact, but are merely 

 approximations of the real (forever unknowable) value. The question 



