SEA-FISHERIES LABORATORY. 177 



axis. We thus find the lengths on either side of the 

 mode within which 50 % of all the fish are placed. Thus 

 the following graph is that drawn from the same frequency 

 distribution graphed as an integral curve in Fig. 1. 

 The mode is at length 20'2 cms. Two vertical lines, 

 one drawn through length 17'8 cms., and the other through 

 length 22'3 cms., so divide up the whole area between the 

 curve and the horizontal axis that the area between these 

 lines is equal to the sum of the two areas outside these 

 lines. We see now, from this particular example, that 

 50 % of all the fish caught were larger than 17*8, and 

 smaller than 22'3 cms. ; 10 % were less than 17"8 cms. in 

 length, and 40 % were greater. If desirable, we can 

 extend the same method so as to find what percentage of 

 the catch were contained within any two other limits of 

 length. This is, of course, not the same thing as finding 

 the " interquartile range," a measure of dispersion often 

 adopted in the treatment of fishery statistics of this kind. 

 The " interquartile range " appears to mean various things. 

 The median value may be taken, that is, that value of the 

 length on either side of which one-half of all the 

 frequencies lie; then the quartiles are found, that is, those 

 values of the length on each side of the median, between 

 which and the median 25 % of all the frequencies lie, and 

 between which and the extreme values of the length there 

 are also 25 % of all the frequencies. Thus the #-axis is 

 thus divided : — 



1 25% 



| 



25% 



1 



25% 



1 



25% | 



lower 



lower 





median 





upper 



upper 



extreme. 



quartile. 









quartile. 



extreme. 



Obviously the range of lengths (#-axis) is not simply 

 divided into four equal parts : the median and quartiles 

 must be found by interpolation, either from the frequencies 

 or from a curve. 



