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 
=fV +n =.1/? In words, this means to multiply each group of 
the frequency distribution (/) by its corresponding value (J), add 
the results, and divide by the total 
number, all of which amounts to 
the adding together of all the 
DISTRIBUTION AS TO LENGTH — 
FINDING THE MEAN? 
r S ris lengths as originally taken and 
5.0 i 5.0 dividing by the total number. It 
5.5 4 22.0 is the usual operation of find- 
6.0 6 308 ing the average, known to every 
- : ee schoolboy, but it is best done 
7.5 31 232.5 methodically, and the method is 
8.0 37 296.0 well illustrated by the case in 
8:5 59 Sens point, as shown in the accom- 
ei . sa panying table. 
iam 3 230.0 By this we see that the aver- 
10.5 II 115.5 age ear in this particular case 
11:0 : 220 was 8.514 inches long, differing 
ee z a oS somewhat from the mode or most 
=2 = 2435.0 : 
frequent length. Eitherthemode 
2435-0 + 286 = 8.514 = J/, the — or the mean can be taken as the 
ics 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 
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 & (capital sigma) is the usual sign of addition or summation. 
5 Here means value, as before, f means frequency, and /V means f x V, 
or the values multiplied by their respective frequencies. 
