140 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
one half of all our counts lay between the limits 11 to 25 and 
one half outside those limits, that is between 7 and 11, and 
between 25 and 41. Usually it would be said that the number 
of colonies on a plate was from 11 to 25, any one of the values 
included in this range being (conventionally) an equally 
admissible value. Expanding these figures we get 550 to 1,250 
as our mean number of organisms present in a mussel. | 
Now this estimate would be a fallacious one: it depends 
on the assumption that the mean is the most probable of all 
the values, and that the deviations in defect of the mean are 
generally equal to those in excess of the mean. In other words, 
the curve of variability of counts of colonies on a plate is 
assumed to be symmetrical (and in theory Gaussian). 
The curve is really J-shaped, that is, extremely asym- 
metrical, as we see by grouping the counts, as follows :— 
No. of Colonies = 6-10, 11-15, 16-20, 21-25, 26-30, 31-35, 36-40, 41-45 
Frequency = 6 3 4 3 2 0 1 i 
The most probable range of counts is 6-10, and the least 
probable is 41-45. This means that we must find some other 
estimate of error due to random sampling. Curves of vari- 
ability are often so nearly symmetrical as to make the method 
just described an admissible one, but in this case (and theory 
suggests that the result is to be expected) the curve is asym- 
metrical to the extreme degree, and the concept of a standard 
deviation has no meaning and is misleading. | 
We can deal with these figures by a graphic method which 
appears to be as accurate (all the circumstances being con- 
sidered) as it need be. We make a new “summational ” 
curve by adding, in succession, the frequencies from the — 
right-hand term, thus :— 
No. of Colonies = 6-10, 11-15, 16-20, 21-25, 26-30, 31-35, 36-40, 41-45 
Prequency = 6 3 4 SH mifes 972 0 1 1 
Summed frequencies= 20 14 11 Fi 4 2 2 1 
