FORMULAS FOR CALCULATING NUMBER OF FRUITS 
REQUIRED FOR ADEQUATE SAMPLE 
FOR ANALYSIS! 
F. E. DENNY 
When taking samples of variable fruits, as oranges for example, 
it is important to obtain an approximation of the number of fruits 
that should be included in the sample, in order that the results of 
the analyses shall be sufficiently accurate for the purpose of the 
investigation. It is the object ot this paper to give formulas which 
may be used in such cases; to illustrate their use by numerical 
examples; to indicate the reliability that may be placed upon them; 
and to show the results that were obtained in applying them to 
the analysis of citrus truits. 
The first step consisted in obtaining a measure of the cabiability 
of the fruit in question. In the case of citrus, this was accomplished 
by analyzing individual fruits, since one fruit was found to yield 
enough material for the analytical work performed. It smaller 
fruits, such as plums, were used, it would be necessary to increase 
the sample to half a dozen, or a dozen, or some other number that 
would make a convenient sample with which to work, but the results 
of the analysis of each of the chosen units should be tabulated 
separately. From these data the probable error of a single sample 
was found, and this value formed the starting point for the calcula- 
tions made in formulas described in later paragraphs. 
Variability in composition of individual — in 
single sample 
Fifty-one oranges were taken at random from a single tree. 
These fruits were all of good marketable quality, and were appar- 
ently free from diseases, insect injuries, and bruises. They were 
uniform in color, but of course variable in size. The fruits were 
analyzed individually and the results for each fruit tabulated 
t Published by permission of the Secretary of Agriculture. 
Botanical Gazette, vol. 73] [44 
