APPENDIX 



STATISTICAL METHODS 



BY H. L. RIETZ, PH.D. 



Assistant Professor of Mathematics, University of Illinois 



SECTION I INTRODUCTION 



An elementary account of the mathematical theory of statistics in a 

 treatise on Thremmatology needs no justification after the foregoing text. 

 The doctrines of evolution and heredity rest on a statistical basis, 1 because 

 we are, in general, concerned with groups of individuals, and with occur- 

 rences of such a nature that, although we cannot make definite quantitative 

 statements about any one of them taken singly, we can make statements 

 in regard to a large number of them taken together with a degree of cer- 

 tainty which increases as the number increases. For example, a thousand 

 ears of corn may vary in length from three inches to eleven inches and 

 have an average (average to be defined in Section II) length of 8.5 inches. 

 We cannot state with any degree of certainty the length of an ear selected 

 at random out of this group of a thousand ears ; but if we select at random 

 five hundred ears out of the thousand we can assert with considerable confi- 

 dence that the average length of the five hundred ears will differ but little 

 from 8.5 inches. 



The important questions in every case are these : In what way can we 

 best describe a population whose variates we have measured ? How can 

 we give the meaning and information contained in this mass of figures in 

 a few words or symbols ? 



A glance at the figures may give a personal impression, but this is not 

 reliable, as is proved by the fact that two persons may each get a very 

 different personal impression, even when examining the same set of figures. 

 We must here resort to more exact methods, and it is the object of this 

 appendix to present in a brief and elementary manner the mathematical 

 methods of dealing with such masses of figures. 



SECTION II AVERAGES 







Meaning and function of an average. The fundamental questions which 

 arise in the discussion of averages are: (i) What is meant by "the aver- 

 age of a system of variates " ? (2) Why do we make use of averages at 



1 See Karl Pearson, Grammar of Science. 

 68 1 



