VOLUME VARIATION OF BOTTLED FOODS. 

 Table 3. — Variations in capacity of bottles — Continued. 



13 



Refer- 

 ence 

 No. 



Size 



of 



bottle. 



Type. 





Capacity at top. 





Number 







Average 









meas- 









devia- 



ured. 



Maxi- 

 mum. 



Mini- 

 mum. 



Average. 



tion. 





Fl. oz. 



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. 



1004-M 



1004-1 



1004-2 



1004 



1015-A 



1015-B 



1004 



1014 



1004 



1004-TJ 



1004-W 



Fl. oz. 

 2 

 2 

 2 

 4 



MACHINE BLOWN. 



Round packer 



do 



do 



Prescription 



Catsup 



Grape juice 



Oval prescription . 



do 



do 



do , 



do 



Fl. oz. 

 "6.012 



.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 

 & given variation is found by the formula / = —, where /is a factor 



whose probability value is read from a table of probability integrals, 

 at 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 



