SERIATION AND PLOTTING OF DATA. 



11 



arises concerning the inclusiveiiess of a class the class range. An 

 approximate rule is : Make the classes only just large enough to have 

 no or very few vacant classes in the series. Following this rule we get 



3.0-3.4; 3.5-3.9; 4.0-4.4; 4.5-4.9; 5.0-5.4; 

 Classes.... 



Frequency 



Classes.... 



Frequency 



The classes are named from their middle value, or better, for ease of 

 subsequent calculations, by a series of small integers (1 to 9). 



In case the data show a tendency of the observer towards estimating 

 to the nearest round number, like 5 or 10, each class should include one 

 and only one of these round numbers. 



As Fechner ('97) has pointed out, the frequency of the classes and all 

 the data to be calculated from the series will vary according to the 

 point at which we begin our seriation. Thus if, instead of beginning the 

 series with 3.0 as in our example, we begin with 3.1 we get the series : 



[ 3.1-3.5; 3.6-4.0; 4.1-4.5; 4.6-5.0; 5.1-5.5; 



Classes.... 

 Frequency 

 Classes .... 



3.3 



1 



( 5.6-6.0; 

 ( 5.8 



3.8 

 1 



6.1-6.5; 

 6.3 



4.3 



4 



6.6-7.0; 

 6.8 

 1 



4.8 



3.5 

 6 



7.1-7.5; 



7.3 



Frequency 6211 



which is quite a different series. Fechner suggests the rule: Choose such 

 a position of the classes as will give a most normal distribution of fre- 

 quencies. According to this rule the first distribution proposed above 

 is to be preferred to the second. 



In order to give a more vivid picture of the frequency of 

 the classes it is important to plot the frequency polygon. 

 This is done on coordinate paper.* 



The best method, especially when the number of classes 

 is less than 20, is to represent the frequencies by rectangles 

 of equal base and of altitude proportional to the frequencies. 

 Lay off along a horizontal line equal contiguous spaces each 

 of which shall represent one class, number the spaces in order 

 from left to right with the class magnitudes in succession, 

 and erect upon these bases rectangles proportionate in height 

 to the frequency of the respective classes (Fig. 3). 



* This paper may be obtained at any artists' supply store. 



