]2 STATISTICAL METHODS. 



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 



Classes ... 

 Frequency 



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 : 



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.* 



A different method should be adopted according as integral 

 or graduated variates are.unler consideration. In the case of 

 integral varia'cs proceed as follows : At equal intervals along 

 a horizontal line (axis of X) draw a series of (vertical) ordinates 

 whose successive heights shall be proportional to the frequency 

 of the classes. Join the tops of the ordinates. Thus for the 

 example given, the curve will be as shown in Fig. 21. This 

 method of drawing the frequency polygon is known as the 

 method of loaded ordinates. 



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



