236 



Annals of the South African Museum. 



The range of variation in the Strandloopers is from 1,185 cc. to 

 1,515 cc. and in the Bushmen 1,060 cc. to 1,570 cc. 

 With these may be compared : — 



Hottentot 1,365 cc. 



Eastern Bantu 1,520 cc. 



Western Bantu 1,420 cc. 



STANDARD DEVIATION. 



The average, whether of index or dimension, is very liable to 

 be affected by a chance occurrence when the total number of 

 observations is very small. To in part eliminate this the study 

 of the standard deviation and of the probable error of the averages 

 has been inti-oduced. The method consists in determining the error 

 of the mean square. As an example the standard deviation of the 

 cephalic index of the Bushman skulls is worked out. 



The average index of the series can be seen by inspection to be 

 somewhere near 75, so this number being taken as a centre, all 

 the other indices can be treated as so many units above this that 

 is positive, or below or negative. The products ZX of the number 



