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BEI.L SYSTEM TECHNICAL JOURNAL 



definitely wherein the method is sadly deficient as a quantitative 

 measure, and therefore often misleading; whereas in certain instances 

 it may be, nevertheless, the only practical method that can be useil. 

 Graphical Method. The graphical method itself may be subdivided 

 into two parts. Let us consider first the plot of the observed and 

 theoretical frequencies. As an example of the unsatisfactory nature 

 of this form of comparison, it is of interest to consider certain data 





"3 a % 7 % ^~ 

 i\ur*fBze or Successes 



Fig. S 



given by Yule '' in which 12 dice are thrown 4,096 times, a throw of 

 4, 5, or G points being reckoned a success. If the dice are symmetrical 

 p = q = Y2. and the theoretical distribution if given by 4,090 (,'2+}2)'"- 

 the terms of which as given by Yule are presented in the third column 

 of Fig. 8. It is suggested that the reader, before going further, 

 consider the graphical and tai)ul,ir representation of these (lat.i. 

 The smooth curve is the theoretical distribution 4,09(3(3 2+' -i)'-- 

 It has been the author's experience to find that in practically every 

 instance in which this curve has been shown to an individual for the 

 first time that the impression is that which Yule evidently desires 

 to produce by the illustration: that is there is a very good fit between 

 theory and practice. This distribution is, however, not symmetrical : 

 it is skew. The dice used in this experiment were not symmetrical: 

 that is, p=f=q. How do we know that these statements are true? 

 Let us consider the normal and second approximation as gi\en 



"Yule — "Introduction to the Theory of Statistics." 



