VOLUME VARIATION OF BOTTLED FOODS. 13 
Table 3. — Variations in capacity of bottles — Continued. 
Refer- 
ence 
No. 
1004-M 
1004-1 
1004-2 
1004 
1015-A 
1015-B 
1004 
1014 
1004 
1004-U 
1004-W 
Size 
of 
bottle. 
Fl. oz. 
2 
2 
2 
4 
8 
8 
8 
8 
12 
16 
16 
Type. 
MACHINE BLOWN. 
Round packer.... 
do 
do 
Prescription 
Catsup 
Grape juice 
Oval prescription 
do 
do 
do 
do 
Capacity at top. 
Number 
Average 
meas- 
devia- 
ured. 
Maxi- 
mum. 
Mini- 
mum. 
Average. 
tion. 
Fl. ozi 
Fl. oz. 
Fl. oz. 
Fl. oz. 
50 
2.44 
2.37 
2.40 
0.013 
50 
2.44 
2.37 
2.40 
.012 
50 
2.42 
2.37 
2.40 
.011 
50 
5.75 
5.44 
5.57 
.068 
50 
8.15 
7.81 
8.05 
.06 
50 
8.69 
8.48 
8.57 
.04 
50 
9.02 
8.72 
8.86 
.07 
50 
8.82 
8.52 
8.72 
.04 
50 
10.75 
10.48 
10.65 
.05 
50 
17.17 
16.70 
16.97 
.09 
25 
17.58 
17.31 
17.47 
.05 
Average 
of 
average 
devia- 
tions of 
the size. 
Fl. oz. 
0.012 
.068 
.05 
.05 
Measurements were taken on a variety of types of bottles, the num- 
ber measured in every set was usually 25 or 50, and several sets of 
data were usually collected on one size of bottles. The maximum, 
minimum, and average capacities to the tops of the bottles show the 
usual range of capacities. The average deviation is the average of 
all the variations from the average capacity of the set as measured. 
The average of the average deviation of the various sizes, as shown 
in the last column, is an index of the variation of the bottles of the 
size mentioned. The figures in this column are used to compute the 
chance of occurrence of the calculated maximum variation in the 
capacity of bottled foods. 
The chances of occurrence of variations in a normal frequency dis- 
tribution are calculated in accordance with the laws of probability 
as found in standard textbooks (3). The probability of occurrence of 
x 
a given variation is found by the formula / = -, where /is a factor 
whose probability value is read from a table of probability integrals, 
x is the limiting variation whose probability of occurrence is de- 
sired, and r is the probable error of a single observation of the dis- 
tribution. The complement of the equivalent of / gives the prob- 
ability that variations greater than x will occur, and the resulting 
fraction, reduced until its numerator is one, gives the chances of their 
occurrence. 
The variation for which it is desired to determine the chance of 
occurrence is the calculated maximum variation given in Table 9. 
This figure is given in Table 4 in the column headed "a?." The prob- 
able error as found experimentally is computed from the last column 
of Table 3. For practical purposes, the probable error is equivalent 
to 0.8453 times the average deviation. It is so computed and in- 
cluded in Table 4, under the column headed " r" The remaining 
