118 Pearl and Surface. 



(jiiintile Distribationt^. 



It would be possible to gain some ideas regarding- the problems 

 discussed above b}' plottine the several frequency distributions, and then 

 noting the position of individual plants in each successive distribution. 

 Such a method, however, would give us but little idea of the general 

 tendency of any group of plants. The best method of attacking these 

 problems has seemed to be, first to divide each frequency distribution 

 into percentiles, and then to follow the groups of plants which fall in 

 these several areas. In this way one can study the relative variability 

 of individual plants in the successive stages entirely apart from the 

 change in absolute size. 



While all plants increase in absolute size with the advance in 

 the season, there are always some plants which are relatively smaller, 

 for example, than the remainder. If it is determined, for each 

 measurement, which plants fall in the lower one -fifth of that frequency 

 distribution, these will be the relatively small plants in each case. 

 Now is it the same plants which occupy this lower one -fifth of each 

 distribution? Or are the plants which are at this end of the first 

 distribution just as likely to lie somewhere else in the succeeding 

 distributions? 



Considering the number of plants in each series it has seemed 

 best to divide each distributiou into five parts or quintiles. In doing 

 this each frequency distribution was divided at such points that each 

 of the resulting five parts has the same area, in other words one-fifth 

 of the number of plants in the given series fell in each quintile. The 

 quintiles are numbered I, II, III, IV and V, beginning at the lower 

 end of the range. In any distributiou the relatively small plants are 

 in (luiiitile I and the relatively large ones in quintile V. 



The exact meaning of a quintile will be made clearer liy the 

 accompanying diagram (Fig. 5). In this diagram a normal curve has 

 been divided into five equal areas by the four perpendicular lines. 

 The frequency in any one of these areas is equal to the freipiency in 

 any other. 



The ungrouped data have been used in determiuing the quintile 

 limits. Even with ungrouped measurements it has been impossible to 

 make all the areas exactly equal. This is always likely to be the case 

 when one is dealing with discrete variates and not large numbers. Thus, 

 in two of the series there are fifty-four plants. If these are divided into 



