362 Quantitative Characters 



est corolla length in the Fi is 34 mm and the largest is 46, 

 whereas the F2 plants range from 22 mm at one extreme to 64 at 

 the other. The variation of a population cannot be determined 

 from the mean alone, and the best method of determining this 

 characteristic of a population is the standard deviation. 



The method of calculating o- is slightly longer than that for 

 the mean. Unless one class coincides with the mean, each class 

 deviates from it to a greater or lesser extent. The deviation is 

 determined for each class. If it is adjusted for differences in 

 frequencies by multiplying each deviation by its frequency and 

 if the values for all classes are summated and if the sum is 

 divided by the number of individuals, a measure of variation 

 known as the average deviation is arrived at. The standard 

 deviation is somewhat similar but is mathematically better. It 

 consists of squaring the deviation of each class, of adjusting each 

 squared deviation for the frequency of the class, averaging these 

 values, and then extracting the square root of the average. The 

 formula is 



n 



and the value for corolla lengths of the Fi is computed in Table 

 21. 



When we observe both the mean and the standard deviation 

 of our Fi and F2 populations, we have a much clearer under- 

 standing of their relationship than we possibly could from the 

 mean alone. The standard deviation of the F2 is considerably 

 larger than the standard deviation of the Fi. AVhen we observed 

 the actual distribution of the two populations in Table 19, we 

 saw that the range of the F2 was much greater than the range of 

 the Fi, and we concluded that the Fo shows greater variability. 

 The standard deviation gives us the same information, is much 

 more reliable than the range, and is much more convenient than 

 a graphic representation of the distribution. Furthermore, it is 

 an important constant in the derivation of some other constants. 

 In general, we can say that other things being equal, the larger 

 the standard deviation, the greater the variability. 



Coefficient of Variability 



At times it is desirable to compare the variability of two 

 things measured in different units. For example, we may wish 



