332 Method of estmiatmg Bacterial Density 



Two statistics were calculated from each set of plates. If x stand for 

 the number of colonies on each plate, and n for the number of plates, 

 the necessary statistics were : 



the mean x ^ S (x), 



n ' 



and the variance v = =- S (x — .r)^, 



n — \ 



where S stands for summation. 



The values of v, being the estimates of the variance from small 

 samples, were inevitably afEected by large samphng errors, which 

 depended upon the number of plates. The whole body of four-plate sets 

 was therefore divided into groups, according to the value of x. Thus for 

 the two groups of four-plate sets having a mean number of colonies 

 65-75 and 75-85, the following values of v were obtained : 



Table IV Table V 



65-75 75-85 



Two facts are apparent from these results (1) the variabihty of v is 

 so great that accurate values are not obtained from the means of about 

 10 values; (2) the difficulty of estimating the variance for given values 

 of X is still further increased by the occurrence of occasional very large 

 values of v. The values of v in sets 51 and 60 in Table IV are much 

 greater than the other 10 values in the same group. The values of the 

 means obtained by excluding and including these high values are given 

 at the foot of the table. 



The first difficulty could be overcome by fitting to the actual values 

 obtained a smooth curve representing the mean ^j for given x; before 



