Distribution as to Length 

 finding the mean 3 



108 DOMESTICATED ANIMALS AND PLANTS 



frequency, and that is the average of all the measurements, 

 technically called the mean. 1 The formula for the mean is 

 2/F-r- n = M? In words, this means to multiply each group of 

 the frequency distribution (/) by its corresponding value ( V)> add 



the results, and divide by the total 

 number, all of which amounts to 

 the adding together of all the 

 lengths as originally taken and 

 dividing by the total number. It 

 is the usual operation of find- 

 ing the average, known to every 

 schoolboy, but it is best done 

 methodically, and the method is 

 well illustrated by the case in 

 point, as shown in the accom- 

 panying table. 



By this we see that the aver- 

 age ear in this particular case 

 was 8.514 inches long, differing 

 somewhat from the mode or most 

 frequent length . Either the mode 

 or the mean can be taken as the 

 type, according to the needs of 

 the case, but the measure most commonly accepted as best rep- 

 resenting the type is the mean or average of all. 



The typical individual. Having determined the type as to a 

 single character, it can be determined in the same way for any 



2435.0 + 286 = 8.514 



mean 



M, the 



1 The mean is to be distinguished from the median, which is the middle- 

 most ; that is to say, if these 286 ears should be spread out in a row, beginning 

 with the shortest, the median would be the ear at the middle point, with as 

 many above it as below it in length. As our number is even, there would be 

 no true median, for the 143d ear would have 142 below it and 143 above it. 

 If there were one ear less, the median would be the 143d ear, and its length 

 would be the median length. 



- The Greek 2 (capital signu) is the usual sign of addition or summation. 



* Here F means value, as before,/ means frequency, and/Fmeans/ X V, 

 or the values multiplied by their respective frequencies. 



