67 



curvature and find the point where the chord, as given on the 

 graduated line, is of least length. This point is approximately 

 the portion of greatest curvature. Drop a perpendicular from 

 this to cut the horizontal axis and the point of intersection, 

 read off on the scale of lengths, will be the abscissa of the point 

 of inflexion on the frequency curve. 



Measures of Dispersion. 



There are a number of such measures — for instance. 

 Standard Deviation , Probable Error, Interquartile Range, Semi- 

 Interquartile Range, etc. We cannot properly speak about 

 " the length " of the plaice inhabiting any sea area in any 

 particular period of time for these lengths may be anything 

 between the extreme lengths actually observed. But we see 

 that all these sizes of plaice do not occur with equal frequency — 

 for instance, the table on p. 61 shows that the plaice on the 

 area in question, and at the particular time, ranged from 

 13 to 33 cms. in length. Nevertheless, about 25 per cent, of all 

 were over 20, but less than 22 cms. in length. Evidently, then, 

 we attach importance to a limited range of lengths, the ends of 

 which are situated somewhere on each side of the maximum 

 of the distribution : this range gives us the prevalent length of 

 the fish at that time and in that area. 



The commonly used measures of dispersion are con- 

 ventional ranges of this kind. The " probable error " and the 

 " interquartile range " are supposed to represent a short range 

 of lengths near the mean length (or near the mode, or near the 

 " median "), such that within this range are contained one-half 

 of all the fish in the sample. The " probable error " is cal- 

 culated from the " standard deviation," which is calculated on 

 the assumption that the frequency curve representing the 

 distribution is what is called the " Gaussian " one. It seldom 

 is in any of the distributions that we have found. Therefore 

 the use of the standard deviation and probable error has no 

 theoretical justification, and, indeed, it may be very misleading. 



