April, ’24] hartzell: interpretation of codling moth data 187 
causes of such variation are seldom known, therefore, it is assumed that 
they occur fortuitously, i. e., they are perfectly random, since they show 
no regularity or periodicity. 
The Measurement of Variation 
% 
Averages are used universally and the arithematical mean is the one 
generally calculated. An average gives no idea of the distribution of 
the observations, so some measure of the “scatter” of the values is 
needed. A valuable as well as common measure of variation is the 
standard deviation which has certain mathematical properties from whch 
are derived two other measures of variation: the coefficient of variability 
and the probable error. The standard deviations and coefficients of 
variability for the several plats shown in Table 1 are given in Table 2. 
Table 2. Standard Deviations and Coefficients of Variability of Infesta¬ 
tion by Codling Moth in the Plats shown in Table 1. 
Plat 
Standard Deviation Coefficient of Variability 
Total Infested Apples 
Check 
163.00 ±77.74 
16.41 ±5.68 
1 
160.15±44.10 
31.45 ±8.21 
2 
283.55±51.12 
37.16 ±7.08 
3 
100.29±19.53 
Worthless Apples. 
26.30 ±5.06 
Check 
108.00 ±51.51 
22.09 ±7.80 
1 
46.73 ±12.87 
23.48 ±5.90 
2 
66.63±12.01 
42.17 ±8.28 
3 
35.45 ±6.90 
34.46 ±6.91 
Probable Error. Assuming, for the purpose of illustration, that no 
systematic error affected the plats (Table 1), it is desired to compare the 
effect of an increased amount of arsenate of lead in the control of the 
codling moth (Plats 2 and 3). All the plats except the check,, received 
the same application up to the time of the codling moth application, 
when plat 2 was sprayed with lime-sulphur with lbs., of dry arsenate 
of lead in each 100 gallons of material, and Plat 3 received an application 
of lime-sulphur having 5 lbs., of dry arsenate of lead to each 100 gallons 
of liquid. Plat 2 has a mean of 158.00 worthless apples 2 and Plat 3 has a 
mean of 102.86 worthless apples. With no other data to assist in the 
comparison, it would seem that the additional amount of lead produced 
2 It has seemed desirable to classify the infested apples in two catergories; viz, 
“Total Infested” and “Worthless”. “Total Infested” includes all fruits showing 
any form of codling moth injury “stings”, while not suitable for the New York A 
Grade, find a readysale under other grades, but apples having deep excavations are 
usually worthless except for cider stock. “Worthless fruits include the data in 
Table 1 under the headings “Calyx”, “Side, deep”, and “Second Brood, Side”. 
