VARIABILITY OF A SINGLE CHARACTER 1 1 1 



This gives 0.872 + as the average amount by which ears of 

 this kind of com deviate from their own average length. It is, 

 therefore, a good measure of variabihty, and, taken together 

 with the average, it gives us a good measure of this particular 

 character, because it tells us not only what is the average length, 

 but also what is the general or average tendency to deviate or 

 depart from that length. In other words, we now have a good 

 measure both of type and variability for this single character 

 and for this particular population. 



Standard deviation. The method of calculating variability 

 just described has the merit of brevity and simplicity, but it so 

 happens that mathematicians prefer a slightly different method. 

 This difference consists only in squaring the several deviations 

 before multiplying by their respective values, thus necessitating 

 the extraction of the square root after division by the total 



number ; thus <t = ^— — '^ • This gives a slightly dif- 



ferent value for variability, which, when derived by this method, 

 is called " standard deviation " and is denoted by the small 

 Greek letter a (sigma). The method of systematically calcu- 

 lating standard deviation is shown in the table on page 112. 

 The disadvantage of standard deviation as compared with aver- 

 age deviation is in the additional labor involved in its calculation, 

 but it possesses many mathematical advantages in the solution 

 of complicated problems. It -is, therefore, the expression uni- 

 versally preferred by mathematicians. As the two results differ, 

 the student must choose between them. The average devia- 

 tion is so seldom used that it is given only as a means of ex- 

 plaining standard deviation on the common-sense ^ basis, and not 

 because it will be used by the student. It is better in every way 

 to follow custom in this matter and use the standard deviation. 



^ Mathematicians have a habit of appealing wherever possible to the in- 

 stincts of " common sense " to evidence the reason for many things which, if 

 absolutely demonstrated, would often require complicated formulae and much 

 abstract reasoning. 



