SERIATIOK AND PLOTTING OF DATA. 13 



EXAMPLE. In 1000 minnows from one lake there are found the 

 following frequencies of anal fin-rays: 



789 10 11 12 13 



1 2 15 279 554 144 5 



A = 10.835 ; a = .728 fin-rays. 

 1999 .__ 



K= :*ooo == - 49975 - 



Looking in Table IV we find 3.48 corresponding to the entry 49975. 

 Then the limiting deviation = 3. 48 X. 728 = 2.5334 and the limiting class 

 is 10.835 2.533=8.302; hence the observation at 7 might be excluded 

 in calculating the constants of the seriation ; but it should not be sup- 

 pressed in publishing the data. 



CERTAIN CONSTANTS OF THE FREQUENCY POLYGON. 



After the data have been gathered and arranged it is neces- 

 sary to determine the law of distribution of the variates. To 

 get at this law we must first determine certain constants. 



The average or mean (A) is the abscissa of the centre of 

 gravity of the frequency polygon. It is found by the formula 



in which V is the magnitude of any class; / its frequency; 

 2 indicates that the sum of the products for all classes into 

 frequency is to be got, and n is the number of variates. 



Thus in the example on p. 10: 

 A =(3.2X1+3.7X1+4.2X3+4.7X3 + 5.2X7+5.7X5+6.2X3 



+ 6.7 X 1 +7.2 XI)-*- 25 = 5.24, 

 or 

 AI=* (IX 1+2 XI +3X3 + 4X3 +5X7 +6X5 +7X3+8X1+ 9X1) 



-*- 25=5.08, 

 A = 5.2* + .08(5.7-5.2) = 5.24. 



A still shorter method of finding A is given on page 20. 



The mode (M) is the class with the greatest frequency. 

 It is necessary to distinguish sharply between the empirical 

 and the theoretical mode. The empirical mode is that mode 

 which is found on inspection of the seriated data. In the 

 example, the empirical mode is 5.2. The theoretical mode is 

 the mode of the theoretical curve most closely agreeing with 

 the observed distribution. Pearson 1902 b , p. 261) gives this 



* 5.2 is the true class magnitude corresponding to the integer 5. 



