Series to Frequency Distributions in Space. 397 



If we complete the solution by means of equations (A) 

 we find 



A = 2-730913 /3/ = 3*447G9 7 = 1-00513 

 ft = 8*77876 /3/ = 9*13828 



92 = 1-4888 



2= -0745 



r = -59422 



r' = -60362 



c = 3-3259 



c'=3'6793 



The starting point of the series is at c(l + rq) to the left 

 and c\\-\-r'q) above the mean of our table, i.e., at age 

 12*7474 for spinsters and 12*7079 for bachelors. 



Numerical Example 3. 



The following table gives the actual distributions in 25,000 

 deals of the trumps in the first two hands, in whist with 

 ordinary shuffling *. 



1 







1 



D 

 2 



istribution of 25,000. 



First Hand. 

 3 4 5 



7 



8 











3 



22 



38 76 



05 



26 



12 



4 



240 



1 



5 



43 



159 



380 531 



358 



153 



54 



4 



1687 



2 



20 



183 



740 



1458 



1590 



920 



323 



49 



7 



5302 



. 3 



42 



300 



1451 



2297 



2059 



934 



222 



34 



4 



7403 



n 



54 



542 



1588 



2048 ! 1497 



505 



101 



14 



1 



0350 



cc 5 



45 



378 



906 



920 



500 



139 



25 



3 





2928 



6 



34 



166 



312 



255 



90 



21 



2 







880 



7 



10 



47 



69 



34 



16 



2 









178 



8 



5 



2 



9 



4 













20 





215 



1724 



5202 7440 6371 2950 



852 



166 



20 



25,000 



* Unpublished material of Professor Karl Pearson. 



