FLUCTUATING VARIATIONS 79 



divisions on the base line, erect ordinates representing by their 

 length the number of individuals of each stature, the lower 

 statures to the left, the greater to the right. Now a line joining 

 the tops of the ordinates will form a polygon or (if the divisions in 

 the base line be quarters of an inch) a curve, which will show 

 graphically the distribution of variation in stature in the population 

 measured. If the curve is symmetrical on each side of the highest 

 ordinate, the mode, it is called the " normal curve " ; the average 

 or mean coinciding with the " mode." If there are more varia- 

 tions on one side of the mode, the curve is " skew " ; if there are 

 two maxima or modes, the curve is " dimorphic " ; and so on. 

 In various ways, which are of great practical convenience, a 

 measure of variability can be deduced from the steepness or flat- 

 ness of the curve, and thus we can readily compare the variability 

 of different characters, or of the same character in different 

 groups and at different times. The curves, especially if made 

 year after year, may show the direction in which the species is 

 moving, perhaps the way in which selection is working, perhaps 

 even that the species is splitting up into two subspecies. 



One of the results of measuring large numbers of variations is 

 to show that there is a relation between the amount of a deviation 

 and the frequency of its occurrence. The greater the divergence 

 from the average, the fewer instances are there. Measurements 

 of a large number of soldiers gave Quetelet the following result ) 

 in which the upper line indicates the heights in inches, and the 

 lower line the number of soldiers of each of these heights. 



60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75) 

 2, 2, 20, 48, 75, 117, 134, 157, 140, 121, 80, 57, 26, 13, 5, 3. 



The general symmetry is plain, on each side of the most 

 frequent condition, 67 inches, which is called the " mode." 



Registration of Variations. — " The modern methods of statistics 

 deal comprehensively with entire species, and with entire groups 

 of influences, just as if they were single entities, and express the 



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