138 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
This error might be minimised by taking a larger sample or 
several small samples, but, since the area (and those contiguous 
to it) must be sampled many times in different conditions, 
one small sample at a time will usually be all that can be 
managed. 
The Error of Random Sampling of the Emulsion. 
¢ 
The plates made are “read” after a standard period of 
incubation. The following numbers represent the counts of 
colonies growing on 20 plates, each of which had been inoculated 
with one c.c. taken from 250 c.c. of the emulsion of 5 mussels 
in 250 c.c. of water :—7, 24, 40, 15, 22, 20, 17, 9, 16, 29, 7) 95 
10, 26, 15, 11, 21,17, 10,41. Now what we are trying to find 
is the number of micro-organisms contained in 250 c.c. of 
emulsion, that is, in 5 mussels. We can only (conveniently) 
count the number contained in a rather small fraction (1/250th) 
of this volume of liquid, and we find that there are 7 or 24 or 
y) 
40, and so on, organisms in this “ unit volume” of one e.c. 
Each of these is a real count, an actual fact, a possible value 
for the number of micro-organisms, of a certain category, 
contained in 1/250th part of our sample. 
The obvious procedure is now to find the mean of the 20 
counts. This is about 18, and multiplymg 18 by 50 we find 
the mean number of organisms in our average mussel, that is, 
900. We might let the result go at that, but we may carry 
the investigation a little further by finding one of two statistical 
functions, the probable error of the mean, or the probable 
error of the distribution of the deviations from the mean. To 
obtain these functions we must calculate the standard deviation » 
of the series given, and this is a very simple matter. Having 
obtained the standard deviation, o, we find + 0-67450. on 
which is the probable error of the mean, or + 0-6745 o, which 
is the probable error of the deviations from the mean. 
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