46 BOTANICAL GAZETTE [JANUARY 
value of P.E. mean for any desired number of fruits may be calcu- 
lated by substituting this number for “n”’ in the formula. Thus 
if P.E. sing. has been found to be 0.5, P.E. mean for a sample of 
pom 
The values in table II, giving the odds, may be utilized under 
the two following conditions. In the first place, it may be used 
in connection with the analytical results obtained from a single lot 
of fruit to estimate the degree of assurance that an accuracy 
between certain limits has been attained. For example, the average 
sugar content (in table I) was 10.89. Ifasecond sample of fifty-one 
fruits had been taken at the same time and under the same condi- 
tions, we would probably not have obtained exactly this value. 
twenty-five fruits is 
TABLE Ii* 
TABLE OF ODDS 
Coefficient Odds Coefficient : Odds 
SO a eee 1.co tor SA er ea 44.87 tor 
1 ape Pe ro Bae 2.21 tor Sere ries. 64.79 tor 
pes Penang 4.64 tor S650. ses 95.15 tor 
re eee a to I Po Be] Bere 142.26 tor 
SOc eres 15.95 tor Ae a 215.92 to x 
S00 as a: 22.26tor Aa ee 332.33 tor 
Bo eo. 91.3610 4 | 4:60. 2 519.83 tor 
* The values in this table were selected from a table by PEARL and MINER 
(6). Original article should be consulted for a complete list of values. 
But the P.E. mean, 0.06, indicates that the chances are even 
(1 to 1) that the value found would have been between 10.95 and 
10.83. In addition to this information, table II shows that the 
chances are 9.89 to 1 that the value would have been between 10.89 
plus (2.50.06) and 10.89 minus (2.5Xo0.06), that is, between 
11.04 and 10.74. 
Considering the probable error of a single sample in connection 
with table II, the P.E. sing. was found to be 0.4. This means that 
if one more fruit had been taken, the chances are even that its 
value would have been between 10.89+0.4, and 10.89—0.4. In 
other words, half the fruits in table I should have sugar values 
between 11.29 and 10.49, and half should be outside these limits. 
Table I shows that twenty-four oranges are within these limits and 
