SEA-FISHERIES LABORATORY. 151 



These curves have been drawn and smoothed by mechanical 

 means. If one takes the middle point of the vertical axis 

 (that would be 37/2 in the above series), draws a horizontal line 

 to cut the curve, and then drops a perpendicular from the 

 point of intersection to cut the horizontal axis, a point on the 

 latter is found, which is the median. 



In the example given the median is at 107 ; that is, in 

 half of all the hauls less than 107 fish were caught in any one 

 case, and either 107 or more than 107 in the other half of the 

 hauls. Now, examine the way in which the horizontal axis is 

 thus divided : half of all the hauls give a range of variation of 

 catch which is from to 107, and the other half gives a range 

 which is from 107 to 650. 



Now the smaller, in general, the catches are, the steeper 

 will be the summational curve, and vice- versa. Therefore the 

 range — median will be the shorter the smaller are the hauls, 

 and will be the larger the bigger are the hauls This range 

 — -median may be called the " shortest half range," and 

 obviously it is a measure of the dispersion. 



It should be noticed that a slight change in the curvature 

 of the graph, due to the smoothing, about the place opposite 

 to the mid position on the vertical axis, shifts the position of 

 the median. Such a variability of the constant must be taken 

 into account as a statistical error, but even then the graph 

 obtained by plotting the half-ranges (or the f or J ranges which 

 can be obtained by the same general method) is a better 

 representation of the change in abundance of the fish than 

 are the annual average catches per haul or per hour's fishing, 

 or the triennial averages taken annually. By this method a 

 very big haul (which might raise the average to a great extent) 

 becomes just what it is — one very exceptional result among a 

 lot of ordinary ones. 



The following table, then, gives the Shortest Half-Ranges 

 obtained by the above method. 



