BY H. S. HALCRO WARDLAW. 843 



this standard. This fact is discussed in greater detail later. 



It is interesting to notice that the group of samples ('J8-105I), 

 the mean value of whose percentage of solids not fat is below 

 standard, is not the same as the group (59-70), whose "mixed'' 

 percentage is below standard. Such an instance emphasises the 

 importance, for some purposes, of distinguishing betw^een the mean 

 composition and the composition of the mixed milk. 

 Distribution of Results. 



A knowledge of the distributions of the values obtained for the 

 different i3roperties and constituents of milk is of much greater 

 13ractical importance than information about their mean values, or 

 the extreme ranges over which they may vary. The practical ques- 

 tion which must be answered is : Of a given number of samples of 

 milk, how^ many may be expected to have values of their composi- 

 tion or properties below or above certain limits? 



Although the limits may be chosen arbitrarily, it is useful to 

 have some central value about which to' fix them. The objection to 

 the arithmetic mean, as already stated, is that it is miduly influ- 

 enced by exceptional results. A value which is even more simply 

 obtained than the arithmetic mean, and which is not affected by 

 exceptional results, is the median. The median value of a series 

 of observations is that value, above and below which 50% of the 

 results lie. The position of the median is most easily determined 

 graphically by plotting the values of the observations as abscissae, 

 and the numbers of results below each value as ordinates. The 

 median value is that whose ordinate is equal to half the maximal 

 ordinate. The curve drawn through the points obtamed in a 

 diagram of this kind is usually S-shaped, and was termed the ogive 

 by Galton (1879), by whom this method of examining a series of 

 observations was very extensively used. 



The median, then. Is a convenient central value about which to 

 measure the distribution of a series of measurements. In the 

 following Table are given the numbers of results lying betweeii 

 certain percentage differences from the median values of the com 

 position and properties of the samples of milk under discussion. 

 The numbers of results are expressed as percentages of the total 

 and are given to the nearest whole number. 



