- 17 - 



LATER STAGES OF GADOIDS 



of our work in 1903. This will give us, at least, a general view of the average composition 

 of the catch upon each station, and of the main differences between the several stations. 



It has not even seemed necessary to print at full length the measurements, centimetre 

 liy centimetre, of the tt)tal catch from each station, but these data appeared to require 

 further condensation. 1 have accordingly adopted a method now common in statistical 

 work for describing a group in brief, and have made use of the corresponding terms re- 

 cognised in the science of statistics. We have to deal with the sizes of a very large 

 number of fish measured in successive centimetres, and we proceed as follows: 



We suppose the whole group to be arranged in order of magnitude, from the least to 

 the greatest. We note firstly the sizes of the smallest and the largest individuals, and call 

 these sizes the extremes. Next we call the median size that which has just as many 

 individuals below as above it. In like manner the sizes one-quarter and three-quarters up 

 the series are called the quartiles: and those one-tenth, two-tenths, etc., to nine-tenths 

 up the series are called the deciles. Of these deciles the lowermost and the upper- 

 most are the most important to us, and the only ones which we shall habitually use: they 

 give us those sizes below and above which, respectively, lie the sizes of 10% of 

 our fish. 



Now if we reduce to percentages such data as those which have given us the curves 

 on Figs. 1, 2, etc., and then sum these percentages from centimetre to centimetre, it is 

 obvious that we get numbers, and may get from them a curve, which represent the per- 

 centages of the whole catch which lie above or below any given centimetre of size. In 

 the following example we have taken the total catch of Cod in the small mesh net from 

 the Firth of Forth — choosing the small-mesh records for the sake of brevity, because 

 they extend over a limited number of centimetres in the scale of size; next the percentage 

 number of fish at each centimetre is calculated; and lastly these percentages are summed 

 in both directions. 



Total Catch of Cod by the small-mesh net in the Firth of Forth (all seasons, 1903 — g). 



It is plain that our extreme sizes are at 6 and 31 centimetres, the median size is 13 

 centimetres; the lower and upper quartiles are at 11 and 16 centimetres; and the lower- 

 most and uppermost deciles at 9 and 19 centimetres, or very nearly so. The accom- 

 panying curve (fig. 18) shows that, at least in this case, and it is so generally, a curve 

 drawn from the above seven points would in its main features be identical with one 

 drawn from centimetre to centimetre. We conclude that, for such purposes as the pre- 

 sent, the determination of these seven points, the media:n, the two extremes, the two 

 quartiles, and the first and last deciles, and the preparation of curves drawn from these, 

 will suffice to give us very important information concerning the composition and nature 

 of such a group of fishes as is represented by the catch in a single haul, or in a series 



