296 



PROFESSOR K. PEARSON AND MR. L. N. G. FILON 



PROGRESSION Table. 



An examination of this table brings out several interesting features of the 

 frequency distribution of Mlillerian glands in the fore-legs of swine. If a group of 

 swine were isolated, and found to have a higher mean number of glands, then this 

 group would most probably have an increased possible range, but at the same tirae a 

 decreased variability and a marked increase of skewness. This increase of the 

 possible range with a decreased variability is especially notable, since the rough-and- 

 ready class of statistician is very apt to treat the range observed as a measure of 

 variability ; we have here a case in which the same cause, raising of the mean, 

 produces opposite effects on range and variability. Increase of range, it will next be 

 observed, produces very little effect on any of the physical constants, but such effect 

 as there is, is an increase of them all. To increase the modal frequency is to increase 

 the range and to reduce both the variability and the skewness. Thus the more 

 mediocre swine there exist in any group, the more nearly their distribution will be 

 normal. Change in the variability is the cause which on the whole produces most 

 effect. Increased variability means lowered mean and less mediocrity, but much 

 increased skewness. Finally increased skewness denotes probable increase of range, 

 variability, and mean. 



As we have suggested in a previous illustration the principles of multiple corre- 

 lation easily enable us to predict the probable change in a random selection in which 

 two or more of the characters differ from those of the general population. 



