18 
Research Bulletin No. > 
F,. the F and the F 3 generations. The fact that a blend occurs 
in F x does not mean that blended inheritance obtains. If it did, 
the F 2 and future generations should breed true to the type 
obtained in F x . If, however, the variability of the F 2 generation 
is much greater than that of the ¥ x generation, segregation and 
in the treatment of statistics. Should any reader be unfamiliar with their 
use, it is hoped that the following short explanation will make them clear: 
When variations which are continuous in character are investigated, 
it is necessary to treat them arbitrarily as discontinuous variations. For 
example, in one of our studies of heights of maize plants we have put 
them into three-inch classes. The names of the classes are called the 
class centers. This means that the class whose center is 58 inches in- 
cludes all the individuals from 57 inches to 59 inches inclusive. Any 
series of things thus measured and thrown into classes is known as a 
frequency distribution, the number in each class being the frequency with 
which the class occurs. Then if each class value is multiplied by the 
frequency with which it occurs, and the sum of these products divided by 
the total number, the average or Mean is obtained. Expressed mathe- 
matically, 
^ _ value X frequency 
number 
With these data we are then able to compute a single number that 
expresses the variability of the frequency distribution from this mean. 
This number is called the Standard Deviation and is always denoted by 
the Greek letter Sigma O). It is found by getting the deviation of each 
class from the mean, — all values to the left of the mean being negative 
and all to the right positive, — squaring them, multiplying the squared 
deviations by their frequency, dividing the sum of these products by the 
total number of individuals, and extracting the square root of the quotient. 
Vv T) t V f 
/x - / , where 2 is the sign of summation. The 
n 
value thus obtained is in terms of the unit values used. For example, in 
the distribution of plant heights in the table just mentioned, the standard 
deviation is in inches. To reduce this concrete value to an abstract one 
so that inches may be compared with pounds, centimeters, and so on, one 
has only to divide the Standard Deviation by the mean and multiply by 
100. This gives us a measure of variability expressed in per cent known 
as the Coefficient of Variability. It is the best method we have of express- 
ing variability as a single arithmetical term. 
When terms like the Mean and the Standard Deviation are used, it is 
also convenient for us to know how much confidence to place in them. If 
we have 100 plants in one frequency distribution and 500 plants in an- 
other, common sense tells us to rely more upon the second distribution 
than upon the first. But to say just how much confidence to place in any 
calculated value, we determine what is known as the Probable Error. 
This value is preceded by the plus-or-minus sign ±. It means that there 
is an even chance that the true value is found within the limiting values 
made by adding to or subtracting from the calculated value the Probable 
Error. For instance, we say that a certain coefficient of variability is 
6.49 ± .32. This means that the chances are even that the true coefficient 
of variability is within or without the values 6.49 + .32 = 6.81 and 
6.49 — .32 = 6.17. 
The class of greatest frequency is termed the Mode. When the 
frequency distribution is not symmetrical with respect to the mode it is 
said to be skewed, 
