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Pearl and Surface. 



variability. Similarily the classes hing next to the end classes ought 

 to be similar in this respect. There appears to be some difference in 

 the two latter classes as shown in table 62. However this difference 

 is probably due to the rather small number of variates in each series. 

 In order to test our assumption and to obtain somewhat smoother series 

 it will be permissible to average the standard deviation of the two end 

 classes and also the two classes lying next to these end classes. We 

 can then compare these two averages with each other and with the 

 deviation of the middle class. Table 21 shows these averages for the 

 observed standard deviation and for the theoretical and the differences 

 between the two. 



Table 21. 

 Showing the average standard deviation of similar classes and 

 the differences between the observed and theoretical constants. 



From this table it is seen; (1) that the difference between the 

 observed and theoretical standard deviations is much greater in the 

 end classes than elsewhere. This means that the observed standard 

 deviations are on the average much lower relatively in the end classes 

 than elsewhere. 



2. The difference between these standard deviations is about 

 fifty percent greater in the end classes than in the middle class. The 

 probable errors are so small that there can be no question as to the 

 significance of these differences. 



3. The difference between the theoretical and observed standard 

 deviations in the classes next to the extremes is slightly less than the 

 difference in the end classes. It is, however, much greater than the 

 difference between these constants in the middle class. 



') The probable errors of these averages have been calculated by taking n = the 

 sura of all the variates entering the average. 



