26 STATISTICAL METHODS. 



a 2 = 18.0448 - 3.7965 = 14.2483. 

 3.7965 X 17.9857 



18.0448 



14.2483 X 17.9857 

 18.0448 



= '8401- 



2000 (18.9846) |/17\9846 0833(.0556 - .2643 - .0704) 



X 2.1(1828 



^n X 3.7840 X 14.2006 

 = 475.24, the number of cases in the modal class. 



The equation of the theoretical curve is thus 



3-784 / r \ 14-201 



where x is the difference between the class magnitude and the 

 regarding signs. 



Position of the mode, y = M d = 3.501 - .523 - 2.978. 



The mean percentage deviation of the theoretical ordinates from the 



observed ordinates is 11. 4#* (Method A). This is calculated as follows: 



V f y & % 



observed theoretical 



- 1 0.0 0.0 



15 21.1 6.1 40.7 



1 209 185.8 +23.2 11.1 



2 365 395.1 30.1 8.2 



3 482 475.2 + 6.8 1.4 



4 414 405.6 + 8.4 2.0 



5 277 272.1 + 4.9 1.8 



6 134 147.6 13.6 10.2 



7 72 65.9 -f 6.1 8.5 



8 23 24.1 2.1 9.5 



9 8 7.0 + 1.0 12.5 

 10 2 1.6 + 0.4 20.0 



11 0.2 - 



12 0.0 11.4* 



MULTIMODAL, CURVES. 



Multimodal curves are given when the frequency in the 

 different classes exhibits more than one mode. False multi- 

 modal curves result from too few observations, or when the 

 classes are made too numerous for the variates. By increas- 

 ing the number of variates or by making the classes more 

 inclusive some of the modes disappear. 



* The mean percentage deviation by Duncker's determination with 

 method B using the same data is 1.73# of area. 



