Ixxiv Tables for Statisticians and Biometricians [XLIX — L 



use of a factorial table is extremely varied, especially in problems in probability 

 involving high numbers. 



Illustration. In a certain district the number of children born per month 

 is 662 and the chance of a birth being male is -ol and of its being female '49. 

 Evaluate the chance that in a given month there should be an equal number of 

 boys and girls born, and compare it with the chance of the most probable numbers 

 (338 boys and 324 girls) being born. 



The chance of equal numbers of boys and girls being born is : 



1662 



C, = C51)»'C49r|33^j|33, . 



Therefore _ 



1 o- f = 'VM 1 i''^07,5702| + 1.581-714,61.56 

 °^ " ~ " 1+ l-690,1961j - 1383-941,4114 

 where the logs of the factorials are found fi-ora Table XLIX. Hence 



log (7,= 200-660,64.53) _ 2.43 



+ 197-773,2042P^*-^'^'^*-^^ 



or Ce = -027155, or once in about 36-8 months, say once in three years the records 

 may be expected to show equal numbers of boys and girls born in the month*. 



The chance of the most probable number of boys and girls is given by 



1662 

 0. = (-51)- (-49)3^ 3^, 



log C,„= 338 X 1-707,5702 + 1581-714,6156 

 + 324x1-690,1961- 709645,9652 

 - 674-359,6453 

 = 21)0-782,26401 s..qi opoi 

 + 197-709,005ir^*^^'^'^^^- 

 Or 6'„i = 030993, or the most probable numbers will only be born once in 

 32-3 months, or say once in two years and eight months. 



We have Ce/C„i=-876, or the chance of equal boys and girls is 88^ of the 

 chance of the most probable numbers of boys and girls. 



Table L (pp. 102—112) 



Tables of Fourth- Moments of Subgroup Frequencies. (Calculated by Alice Lee 

 and P. F. Everitt ; published here for the first time.) 



In the usual method of determining the raw moments of a frequency, we take 

 moments about an arbitrary origin, which is towards the apparent mode and 



* Actually of course the problem is more complex, because the number of children born per mouth 

 is not constant. 



