360 Quantitative Characters 



the results are exactly the same in either case. Similarly, the 

 value 40 is multiplied by 24, and 43 is multiplied by 16. The 

 student 'may wonder why no plants are listed with corollas 35, 

 36, 38, 39, 41, 42, 44, or 45 mm long. Certainly, corolla length 

 is not always found in units of 3 mm. For purposes of handling 

 data, however, it is customary to group our individual values 

 into classes. Any fallacies that this might introduce are small 

 and are more than justified by the simplicity of this computation 

 method. When breaking up our array of figures into classes, 

 arbitrary class ranges must be chosen which must be the same 

 for all classes. East, for example, chose 3 mm as his class 

 range. For this Fi family, the classes were 33-35, 36-38, 39^1, 

 42-44, and 45-47. The values listed in Table 19 are the class 

 centers, and these are the values that are used in determining 

 the statistical constants. Obviously, the class center is just half- 

 way between the two extreme values of the class. To determine 

 the mean, each class value (V) is multiplied by the frequency 

 of that class (/). The sum, 2, of these products is divided by 

 the number of individuals. The formula for this is 



_ '^fV 



X = 



n 



and the actual calculation is worked out in Table 21. The stu- 

 dent is further reminded that formulae should be understood 

 and not merely committed to memory. 



Standard Deviation 



The second column of constants in Table 19 represents the 

 standard deviation, which is usually designated by a lower-case 

 Greek sigma, o-. The mean gives us a considerable amount of 

 information about a population and helps us to compare two 

 populations. A glance at the means of the two Pi and the Fi 

 generations in Table 19 shows us that all three populations are 

 considerably different from one another. The plants of Pi (1) 

 have corollas only about 21 mm long, those of Pi (2) have corol- 

 las about four times as long, and the corollas of the Fi family 

 have an average length nearly intermediate between the other 

 two. Such information is very helpful. 



When we examine the means of the Fi and F2 populations, 

 we are led to believe that (so far as the average length of the 



