36 



GENETICS IN RELATION TO AGRICULTURE 



The significance of the normal curve as an index of variation is based 

 on the conception that the area within the curve represents an indefinite 

 number of individuals and that the constants of the curve indicate the 

 distribution of these individuals with respect to a given character. If 

 in any curve (Fig. 16) the perpendicular erected at M divides the area of 

 the curve into two equal parts, this line is the median and the point M 

 represents the average or mean of all the values from which the curve is 

 constructed. The perfect symmetry of the normal curve causes the 

 median to coincide with the mean and the mode; but in actual cases 



FIG. 16. A normal curve divided 

 into quartiles by the perpendiculars 

 erected at M,Qi,Qa. 



FIG. 17. A normal curve of exactly the 

 same area as the curve in Fig. 16, but with flat- 

 ter slope and correspondingly greater breadth. 

 The distribution pictured by this curve pre- 

 sents a greater range of variation than in 

 Fig. 16 as is indicated also by the value of Q. 



these three values will not coincide because the curve will not be sym- 

 metrical. If a perpendicular be erected in either half of the curve at 

 such a distance from M that it divides the area enclosed by the median, 

 the base and half of the curve into two equal parts, the distance of such 

 a perpendicular, Qi or Q 3 from M is the quartile, q. Then in the normal 

 curve q = MQi = MQ$. Now the slope of the curve is an index of the 

 amount of variability. The steeper the slope supposing the area (the 

 number of individuals) to remain the same, the nearer to the median 

 will be the position of the quartile and hence the position of the quartile 

 is also an index of variability (Fig. 17). Since curves constructed from 

 actual distributions are never symmetrical, in practice the index taken is 



5 However, the measure of variation in common use is the standard 



6 



deviation, a, which in the normal curve represents a distance from the median 



equalt 06745' 



Requirements of Biometrical Study. The data for statistical analysis 

 are obtained by counting, by measurement, or by arbitrary graduation 

 of continuous differences like degree of pigmentation. In order that such 



