FLUCTUATION'S IN THE SUPPLY OF HERRING 
27 
in which a, a u etc., are the averages on various days, S, S h etc., are the standard 
averages, and N is the number of days. Thus D is, for the month in question, the 
geometric mean of the percentages that the averages (a, cq, etc.) of the various 
days are of the corresponding values on the standard curve. The average for each 
month in 1928 has been called 100 per cent and the monthly averages of the other 
years expressed as percentages of this base. 
Table 4. — Comparisons of average daily catches of each year with a standard daily catch curve 
The geometric mean has been used in preference to the arithmetic mean so as 
to give equal weight to the same relation deviations from the standard curve. Thus 
an increase of 100 per cent in a number should have the same weight as a decrease 
of 50 per cent — in one case the number is doubled, in the other it is halved. For 
example, the geometric mean of 200 per cent and 50 per cent (representing a 100 per 
cent increase and a 50 per cent decrease) is 100 per cent, but the arithmetic mean is 
125 per cent. For a detailed discussion of the use of the geometric mean see Fisher 
(1922). 
In comparing the curves in Figure 13 it should be noted that changing the geo- 
metric means of the percentages to percentages of the 1928 mean was done only for 
the purpose of putting all of the curves on the same basis for comparison. These 
curves give the rates of change and therefore the slopes of the various portions are 
directly comparable. 
The month of June (fig. 13) maintains practically the same level of abundance, 
except in 1927 in which Groups I and II show June to be distinctly lower. 
The abundance during the month of July shows a consistent drop from 1926 to 
1927; 1927 and 1928 are practically the same. In 1929 Group I shows a further 
decline, but Group II shows an equally large increase. The only conclusion to be 
drawn is that 1926 shows the highest level of abundance in this month. 
In the month of August it is clear that 1928 shows the least abundance, 1926 
the most. 
