380 SEMI-CENTENNIAL OF TORREY BOTANICAL CLUB 
П. STATISTICAL TREATMENT OF DATA 
The various sources of partial variability considered above 
make clear some essentials in regard to the proper collection and 
utilization of data in order that they may reveal the nature of the 
character of flower number and its hereditary behavior. If the 
flower number per head fluctuated with much the same range from 
day to day, as it does for a few plants of chicory, the mean, the 
standard deviation, and the coefficient of variability would be 
quite sufficient to give an estimate of the individual and could be 
determined from rather random readings with the magnitude of 
error depending chiefly on the number of heads that were counted. 
But this is not the case with the majority of plants. The flower 
heads mature at different dates and the number per head, as а 
rule, decreases as the season advances. It will be shown later 
` this s to some degree related to the position of the head on a plant. 
The partial variations from day to day are not solely fluctua- 
ting. For most plants, as shown in TABLES I, 2, and 41 the daily 
range of fluctuation changes in a somewhat uniform progression to 
lower values. It seems to the writers that this element of change 
should be recognized in any statistical treatment which attempts 
adequately to determine values for a plant as a whole. 
In this investigation, instead of calculating the mean and the 
variability, as expressed either by the standard deviation or the 
coefficient of variability, and using these as expressions to char- 
acterize the flower number of an individual plant, the flower 
number of the first day of bloom and the rate of change have been 
calculated and used. 
The latter expression, as will be seen more clearly presently, 
is calculated as the mean and the variability would be from all 
the data at hand. A starting point, a rate of change, and the 
length of time through which this change takes place, gives an 
index to the variability. Furthermore, one can find the average 
flower number for any one particular day (o, for ta), if the flower 
number is given for the first day of bloom and the rate of change 
following (either positive or negative). We may assume, for the 
present, that the rate of change is uniform and call it b, and we 
shall indicate the flower number for the first day of bloom (which 
is to be calculated) a. 
