HO DOMESTICATED ANIMALS AND PLANTS 



Variability as to Length of 

 Ear — Average Deviation 



To avoid large decimals we discard the last figure and take the 

 mean at 8.51. From this mean the shortest ear, which was 5 

 inches long, deviated 3.51 inches, the next group of four each 



deviated 3.01 inches, or a 

 total deviation of 4 x 3.01 = 

 12.04. Each of the next 

 group of six deviated 2.51, 

 equaling 15.06 in all, and so 

 on for all the groups. It is 

 manifest that if we continue 

 down the distribution in this 

 way, calculating the deviation 

 for each group, and then add 

 all together, we shall have the 

 total amount by which all the 

 ears deviated from the length 

 of their average, and it is 

 equally evident that if this 

 total be divided by the num- 

 ber of ears, we shall have the 

 average deviation of these 

 ears. Such an average is a 

 fair measure of variability with 

 respect to the character length in this particular variety. The 



formula would read as follows : -=^ = average deviation. 2 



The process is carried out systematically 3 in the table above. 



1 All deviations below the mean are denoted by the minus sign. In calculat- 

 ing deviation by this method these signs are disregarded. In the method to be 

 next described these deviations are squared so that the minus signs disappear 

 naturally. 



2 In words this formula means : subtract the mean from each of the values 

 involved, multiply these differences by their respective frequencies (disre- 

 garding the minus signs), add these products, and divide by the total number 

 in the frequency distribution. 



8 In all work of this kind systematic arrangement is desirable, not only on 

 the score of neatness but of accuracy as well. 



Mean = 8.514 



149.42 h- 286 = 0.872 -f, average 



deviation 



