Formula: Average deviation 



d. f 



S^ 



Similarly, the average deviation of the milk production 

 in the 1,200 cows can be shown to be 1,787.3 lbs. (5,515 lbs. 

 being average production). 



The standard deviation, considered by mathematicians 

 to be more convenient as a measure of variability, is calcu- 

 lated in a shghtly different way. In the beans it would 

 be worked out as follows: — 



1 (12-8)2 + 2(12-9)2 + 23 1(2-10)= + 108(12-11)2 + 

 167 (12-12)2 + 106 (13-12)2 33 (14-12)2 + 7 (15-12)2 

 + 1 (16-12)2 -^ 448; and the square root of this quotient 

 gives 1.1 mm. 



Formula: — Standard Deviation 



Sd2.f 

 n 



In the case of the production of milk from 1,200 cows 

 the standard deviation is 1,770.1 lbs. 



For the sake of clearness, the results are summarized 

 in the following table. 



A Comparison of Average and Standard Deviations 

 as to Length of Beans 



V- Value, f= frequency, M= Mean or average. 



M or Average = 5409 



Av. Dev. 



St. Dev = 



448 

 361 



448 

 551 



448 



= 12; 



= .8; 



= 1.1 



FROBABIiZ: EBROB. — In sta- 

 tistical studies of variations 

 the results are usually checked 

 up liy a determination of the 

 Probable Error. (See E.. Daven- 

 port and Babcock and Clausen 

 for details.). 



26 



