51 



The average variation of the successive weights from the average 

 of all the weights, when reduced to a percentage basis, as in the above 

 sample, maybe called '"percentage variation." The figure expressing 

 the percentage variation is useful to indicate the degree of uniformit}'^ 

 in the successive weights of the same article of food and furnishes an 

 approximate measure of the accuracy of the method of averages which 

 lies at the bottom of the whole investigation. The precise meaning of 

 the percentage variation figure is clear from the following considera- 

 tions: Let us suppose that the average weight of all the orders of bread 

 eaten b}' a certain student during three weeks, determined b}' the actual 

 weighing of each order, is found to be 100 grams. Suppose, also, that 

 the average variation of the single orders from 100 grams is 4.7 

 grams; then the percentage variation is 4.7. This working average, as 

 it may be termed, determined by a comparativel}" small number of 

 observations, may or may not be 100 grams, the true average. For 

 example, it may happen that the weights of the orders that we select 

 for weighing are all above the true average or all below, instead of 

 some above and some below. In the iirst instance the working aver- 

 age would be 104. 7 grams, on the assumption that the specimen orders 

 were dished out with the same uniformity that obtained when the true 

 average was determined. In other words, the maximum error that 

 the method is likel}' to introduce is 4.7 per cent of the total weight of 

 the bread consumed. 



Consider now the uniformity shown by other articles of food. For 

 the important class of breadstuffs the percentage variation was found 

 to be 7.6, for cereals it was Q.G, and for dairy products 6.Q. Meats 

 showed the greatest irregularities, the percentage variation being 

 13.5. Averaging the percentage variations of all the important arti- 

 cles gives 8.6 — that is to say, if the same number of orders of all the 

 various dishes were consumed, and we estimate the total weights by 

 nuiltiplying the average weight of each order by the number of orders 

 eaten, the greatest error that lack of uniformity in the individual 

 weights could reasonably be expected to introduce would be about 9 

 per cent of the total weight sought. 



It does not follow, however, that the largest error to be expected 

 in the final figures for protein and energy is 9 per cent, for all the 

 articles of food are not of equal importance in the result. Evidently, 

 if a subject eats but one or two orders of meat during a period, the 

 addition to his average dail}' ration is small, and the error is slight 

 if the item is left out altogether, hence it suffices to determine the 

 nutrients and weight of the meat approximately. Similarly, in a ration 

 consisting of meat and fruit in equal weights, it is unnecessar}^ to deter- 

 mine either the weight of the fruit or its proportion of nutrients with 

 the same accuracy as in the case of meat, since the low value of the 

 fruit in terms of protein and energy makes its effect on the total vahie 



