VARIATION IN DIFFERENT PORTIONS OF PLANT. 



43 



butions for Series I, II, and III in the analytical treatment. The justi- 

 fication for combining these three sets of data will have been apparent to 

 anyone who has inspected the values of the constants which have been 

 given in the preceding tables. The ''raw" moments were used in this 

 as in the other cases. The values of the chief physical and algebraical 

 constants of distributions 188 and 189 of tables 14 and 17 are given in 

 table 20. 



Table 20. — Analytical constants for variation in leaf-number. Series I, II, 



and III combined. 



Constant. 



Primary- 

 branch 



whorls( Dis- 

 tribution 

 No. 188). 



Total frequency 



^2 



f^i 



Ml 



8,-3. 



1360 



1.4183 



— .8671 

 5.3199 



.2636 



.5134 



2.6448 



— .3552 

 —1.5011 



Secondary- 

 branch 



whorls (Dis- 

 tribution 



No. 189). 



539 



1.5753 



— .6964 

 5.3816 



.1240 



.3522 



2.1685 



— .8315 

 —2.0351 



Constant. 



Skewness 



Modal divergence... 

 Standard deviation 



Mean 



Mode 



Range 



Lower end of range 

 Upper end of range 



From this table we note that: 



(a) The distribution for the secondary branches is markedly more 

 skew than is that for the primaries. Consequently, since the standard 

 deviation is also greater in the case of the secondary branches, we find 



that— 



(6) The distance from the mean to the mode is very nearly twice as 

 great in the secondary branches as it is in the primaries. 



(c) Secondary branches have a lower mean number of leaves to the 

 whorl, but a higher modal number than the primaries. Too much stress 

 must not, however, be laid on the fact that the secondaries show the 

 higher modal number, because, as has been pointed out, the values of 

 the moments from which the mode has to be calculated have not been 

 in any way corrected. 



id) The theoretical range of variation is smaller for secondary 

 branches than it is for primaries by more than one leaf. The second- 

 ary curve starts at a higher and ends at a lower value than does the 

 primary. 



(e) The skewness is negative for both curves. 



(/) The kurtosis {v =(^2 — 3) is negative in both curves, but has a 

 considerably higher value in the case of the secondary branches, thus 

 indicating that the secondary-branch distribution is the more flat-topped. 



