SEA-FISHERIES LABORATORY. Ill 



statistics, does not help ns greatly in dealing with true 

 samples. 



By far the best method of graphing the figures is to 

 integrate the percentage numbers and to plot the values 

 so obtained. This was suggested to me by Mr. H. J. 

 Buchanan-Wollaston* and the method has been con- 

 sistently applied in the analysis of the data obtained. 

 The frequencies are summed so that any ordinate, 

 y n = X^y. These values are then plotted in place of 

 the original figures, and each value of y on the curves 

 represents the percentage of plaice at and above the 

 corresponding length represented by x. A glance at the 

 graphs on pp. 117, 124, will at once show how greatly 

 the analysis of the figures is facilitated ; and how 

 regularity is to be obtained from data apparently most 

 irregular. All the curves are very smooth: the dots 

 represent the positions of the actual figures; and the 

 graph can be drawn by inspection without any doubt as 

 to how it ought to go. One sees at once what is the 

 dispersion of the group of fish, and what are the modal 

 sizes. 



The latter values are obtained by determining the 

 points of inflexion on the curves. The graph is drawn 

 very carefully, employing some mechanical method of 

 obtaining a line which passes as near as possible to all 

 the points, with as few changes of curvature as possible. 

 As a rule this is a matter of little difficulty. The tangent 

 is then drawn, using a glass ruler so that both sides of the 

 curve are visible. The curvature is usually very slight 

 at the point of inflexion, but the points where the tangent 

 apparently begins to diverge from the curve can usually 

 be observed fairly accurately, and the actual position of 



* The method is applied by Bowley, Elerne?ils of Statistics, Ed. 2, 

 p. 155, 1902. 



