THE STATISTICAL STUDY OF VARIATION 43 



by the corresponding frequency (f.d'} ; divide the difference between the 

 minus and plus products by n to obtain correction factor (;); then 

 multiply each f.d' by d' to get f.d' 2 ; summate the last products and 

 divide by n; from the quotient subtract w 2 and then extract the square 

 root. The illustration, Table VI, is based upon the same data as the 

 preceding. 



The short method of computing the standard deviation is the 

 more accurate because of the elimination of many decimal places. In 

 addition to the complete short method there is shown in the last 

 column on the right a very useful method of checking the computa- 

 tion. Each f(d f + I) 2 is calculated algebraically. Thus in the first 

 case / = 3 and d' = 3; substituting we have 3( 3 + I) 2 = 12. In 

 the same way 2(/) + 2S(/.rf') + S(/.d' 2 ) is computed algebraically. 

 Substituting we have 400 + (-34) + 701 = 1067. 



The standard deviation, being a measure of absolute variation, is 

 exceedingly useful in comparing the variability of one variety with 

 another with respect to- the same character, or of the same variety in 

 different years with' respect to a given character, or of one character with 

 another in the same or different species. For example, Love and Leighty 

 in their memoir on "Variation and Correlation of Oats" give the means 

 and standard deviations for total yield of plant in grams (as well as for 

 eight other characters) for the same pure strain of Sixty Day oats for 

 three years as follows: 



1909 - M = 4.032, a = 2.249 



1910 - M = 3.458, er = 1.323 

 1912 - M = 7.962, <r = 3.353. 



The differences between these values are due mainly to differences in 

 climatic conditions during the three years, the year 1910 having been 

 especially dry and hot. Similar differences appear in the means and 

 standard deviations for height of plant, number of culms and number of 

 grains produced. This particular observation leads to no new con- 

 clusion as it is well known that climatic conditions profoundly influence 

 crop yield, but it illustrates the significance of the standard deviation 

 as a measure of variation. Furthermore it is of interest to note that 

 drouth not only reduces plant growth and yield in this variety but the 

 amount of variation as well. 



In 1910 the amount of absolute variation was only one-third that of 

 1912. However, the amount of relative variation was not so much 

 affected by drouth as might at first appear. When comparing standard 

 deviations of different varieties or of the same variety under diverse 

 conditions, it should be remembered that the means of the groups under 



