SEA-FISHERIES LABORATORY. 



449 



of them were B. coli. The statistical errors of such an 

 estimation must be reckoned with : obviously, the 

 probable error of the mean count per plate must be 

 calculated, and this may be done by making a trial series 

 of plates, say 10 to 20, and then finding a probable error 

 This is calculated in the following example: — 



Ten plates, each inoculated with 1 c.c. of an 

 emulsion of 5 mussels in 250 c.c. of sterile water. The 

 plates contained 210, 258, 274, 277, 302, 305, 352, 375, 

 453 and 730 colonies. The mean number of colonies 

 is 353. 



The frequency distribution is as follows : — 



X 



/ 



x> 



fx> 



/(*/)« 



Between 200 and 300 colonies... 

 ,, 300 and 400 ,, 

 ,, 400 and 500 

 ,, 500 and 600 

 ,, 600 and 700 

 „ 700 and 800 



4 

 4 

 1 

 

 



1 



-1 

 



+1 



+ 2 

 + 3 

 + 4 



-4 

 



+ 1 

 

 



+ 4 



+ 4 

 



+ 1 











+ 16 





10 





+ 1 



21 



The mean is 350 + 100 x^= 360. 



The standard deviation is 

 100 X 



<J = x«; 



and the probable error of the mean is 

 145 x 0-6745 = 98. 



This means that we may divide the range of values 

 into two parts : (1) a part lying between the mean — 98, 

 and the mean +98, that is, between 252 and 448; and 

 (2) a part between the lower limit of the range and 252, 

 and between the upper limit of the range and 448. 

 Suppose that any single count from a plate is now made, 

 it is just as likely that its value will lie between 252 

 DD 



