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Part III. — Eighteenth Annual Report 



Conversion of Measurements into Percentages. 



In order to admit of a comparison between the measurements made 

 upon mackerel of different sizes, it is necessary to convert them into per- 

 centages of some standard length. The total length of the fish is a 

 convenient standard, in percentages of which the measurements may be 

 expressed. I have adopted that standard. Heincke, however, employed 

 for the herring more than one standard. For measurements made upon 

 the head he took for his standard the length of the head, and so on. 

 This may, or may not, be an advantage, but for the sake of simplicity I 

 have employed only one standard. 



Means of Averages. 



The averages of all the characters were then calculated for all the 

 individuals in each of the one-centimetre divisions. The averages 

 for the males and females are to be found in Table VII. (Aberdeen), 

 IX. (Clyde), and VIII. (Barra), (pp. 315 et seq.). The figure within 

 brackets, alongside each average, indicates the number of individuals 

 from which the average was calculated. The averages of all the 

 males and all the females in respect to each character were then 

 found (Table III.), and this was finally done for the males and females 

 together (vide Tables IV. and IVa). The figures in the vertical 

 columns marked (No.) give the number of individuals from which the 

 average was made. The Standard Deviation (or) and Fluctuation of the 

 Mean (M +_5r) is given for several characters in Table VIIa. In the 

 calculation of these quantities I am indebted to Mr. H. M. Kyle for 

 much assistance. 



[Table. 



