

WEIGHT VARIATION OF PACKAGE FOODS. 13 
the combination of the average deviation from 0 average minus aim 
(a) and the average deviation of single packages from the average 
weight (6), according to the law of propagation of errors, that is, 
J (a)?+ (6)?, where (a) and (6) are constituent errors. The resulting 
chances are given in Table 9. 
With the exception of 3-pound and 5-pound packages, on which 
the data are few, the chances in the last column would indicate that 
the calculated maximum error will seldom if ever occur in actual 
practice. 
The averages of the chances given in Tables 8 and 9 are 1 in 4,551 
and 1 in 2,167, respectively, which, compared to 1 in 1,000, indicate 
that if the packer aims to make his packages meet the declared weight 
it is reasonably certain that neither his average nor his individual 
weights will vary from the declared weight by more than the calcu- 
lated maxima. 
TaBLE 9.—Chances of occurrence of variations greater than the calculated maximum error 
on single packages. 








XS 
Caleu- Average oe 
lated | Average noes BL Chance of occurrence 
maxi- devia- EinaT6 SS of variations greater 
Size of package. mum tion Bae Bs Ge t than calculated 
error on | fromo |? one x 7 maximum, based 
single |average— COED 3 on observed data. 
packages} aim | 97035 eA 
g 3 
(z). (a). (0). (rT). (f). 
Ozs Oz Oz. Oz 
2-OUEiaalelcisieveleseee 0. 150 0. 014 0. 030 028 5.35 | 1 in 3,333 
4-OZicjainicla sieisins wee i - 032 - 023 033 4.55 | lin 476 
S-OZs weiss sieiceis 150 . 023 . 042 041 31065| dina £4 
ll assscaneaaene 213 - 032 - 039 043 4.95 | lin 1,250 
S-lbeestesaee tee 363 . 120 . 094 130 Petr) alatay 0. Alyy 
TAO eS SS anes Nena - 409 - 005 - 169 144 Petes) | lbibal 9 I UfSy 
MM lSesaacsuesose 7. 73 .70 . 40 69 11.2 | lin more than 10,000. 

The fact that the calculated and observed results check as well as 
they do on the sizes on which experimental results were obtained 
justifies a confidence in the calculated figures. In the absence of a 
large amount of carefully taken experimental results, it is believed 
that the figures in the last two columns of Tables 5 and 6, ‘‘Calculated 
maximum error on a single package,” and ‘‘Calculated maximum 
error on the average of a representative sample,’”’ represent a fair 
approximation to the limiting error of good commercial practice as 
outlined in this bulletin when applied to tea, coffee, cocoa, spices, 
and similar granular, free-flowing products. 
HAND WEIGHING VERSUS MACHINE WEIGHING. 
The exceptionally important part which machine weighing plays in 
the development of the package-food industry demands that the pos- 
sibilities of machine weighing be especially considered as a method 


