838 THE VARIABILITY OF COWs' MILK, i., 



To obtain some general idea of the significance of series of 

 figures like those in the above Table, it is usual to calculate from 

 them certain representative or mean values. The commonest form 

 of mean value is the arithmetic mean, and this is meant by the word, 

 unless something else is specified. The arithmetic mean, however, 

 is only truly representative of a series of results when all these 

 results may be considered as equally likely to occur. A few excep- 

 tional results do not really alter a series as a whole, but such 

 exceptional results affect the arithmetic mean value, and their 

 effect becomes more noticeable as these results become more 

 unlikely to occur. Such a mean value, which <is unduly affected by 

 exceptional results, has, therefore, obvious defects as the repre- 

 sentative value of a series. Further, the arithmetic mean takes no 

 account of the manner in which the results in a series are grouped. 

 It gives no information whatever about the distribution of the 

 results withm the series. The arithmetic mean, on the other hand, 

 is very simply calculated, and in series of values that have no 

 definite grouping, it is the only form of mean value which can be 

 obtained. 



Attention may be drawn here to the fact, that the mean values 

 of the composition and properties of a number of samples of milk 

 are not necessarly the same as those of the milk obtained by mixing 

 together all these samples. In calculating the arithmetic mean, no 

 account is taken of the varying sizes of the samples. In mixing 

 together a number of samples, how^ever, the size of each will have 

 an effect on the composition and properties of the mixed milk. As 

 it is the mixed milk, and not a hy^Dothetical mean milk w^hich is 

 sold, the values of the composition of the mixed milk have been 

 calculated, and the figures for them have been inserted in brackets 

 under the corresponding mean figures. As will be seen, the differ- 

 ence between the two figures in no case exceeds 2% of their value. 

 The ''mixed" values of the physical properties have not been cal- 

 culated, as the variation of these is so small, that the differ- 

 ences from the mean values must be even less than in the ease of 

 the composition. 



The sunLs of the percentages of the constituents in the above 

 Table do not exactly equal the percentages of total solids. This 



