Standard and Probable Errors 363 



to know whether the length of the corolla is more variable than 

 the area of the corolla or than the weight of the flower. Since 

 the units of measurement are different, the standard deviation 

 alone cannot be used. The same is also true even if the units of 

 measurement are the same, provided that the two means are 

 significantly different. Plants Pi (2) and the F2 plants have 

 standard deviations that are not far apart, but their means are 

 considerably different. Even in this case, the standard deviation 

 alone cannot be used to compare the two populations. A con- 

 stant that can be used is the coefficient of variability, which is 

 nothing more than the ratio of the standard deviation to the 

 mean of the same population multiplied by 100 so' as to convert 

 the value of the coefficient of variability to the familiar basis of 

 percentage. The symbol for this constant is v, and its formula is 



100(7 



V = 



X 



The coefficient of variability of the F2 is much greater than that 

 of the plants of N. alata (Table 19). 



Standard and Probable Errors 



The standard and probable errors of a constant are important 

 indications of the reliability of that constant. They were dis- 

 cussed for ratios in Chapter 8 and now can be applied to data 

 showing continuous variation. 



In the Fi from the Nicotiana cross, 46 plants were measured; 

 they averaged 40.78 mm in length of corolla. These 46 plants 

 were drawn by chance from a population of infinite size. We 

 could, therefore, choose a great many other samples of 46 plants 

 from this same population of infinite size, and we could also 

 choose numerous samples containing more or fewer plants than 

 46. If we did this, could we expect that the mean corolla length 

 would always be 40.78 mm? The answer is a decided no. If 

 we measured a number of Fi populations, we would obtain a 

 number of different means. If these means were then plotted in 

 the same manner that the original measurements were plotted, 

 we should see that the means would themselves form a frequency 

 curve which, like the other, had most of the means in the central 

 part of the curve and fewest at the ends. 



