[ 268 ] 



XXXIII. The Choice of Means. By F. Y. Edgeworth, M.A., 

 Lecturer on Logic at King's College, London*. 



WHAT is the best Mean ?, is a question which I have 

 elsewhere f attempted to answer generally. A sup- 

 plement to that answer, with special reference to the case of 

 Discordant Observations, is intended here. 



One large class of Discordant Observations belongs to the 

 category of errors whose law of facility is a compound of 

 different Probability-Curves J . According to what is known or 

 surmised about the components, different methods may be 

 appropriate. It is here submitted that very generally, and in 

 the absence of special knowledge about the genesis of the 

 observations, the compound source of error may be treated 

 as belonging to the category of curves other than Proba- 

 bility-Curves § . This category also comprises the species of 

 Discordant || Observations other than that above defined. 



What, then, are the methods proper to this category ? They 

 are two — the Method of Least Squares and the Method of 

 Situation^. The Method of Least Squares is a good method **, 

 for the same reason that it may be a good plan for an Insu- 

 rance Company to deal with a tailor or farmer according to 

 the general statistics for adult healthy males of the same age 

 and country ; if it is either impossible to obtain, or not worth 

 while to utilise, the special vital statistics for the different 

 occupations. What corresponds in our case to the abstracted 

 attribute of occupation, is the generally unknown form of the 

 facility-function and the ignored mutual distances between 

 the given observations. What corresponds to the attributes 

 retained by the Insurance Company is the Arithmetic Mean 



* Communicated by the Author. 



t " Observations and Statistics " (Cambridge Philosophical Transac- 

 tions, 1885), corrected by the Appendix to Metretike (London Temple 

 Publishing Company, 1887). 



X In the notation of the paper referred to, a c defy. See examples in 

 the paper on Discordant Observations in this Journal, April 1887. 



§ More exactly in the notation proposed by the writer, acdegh; that 

 is, (a) relating to an objective (not fictitious) Mean, (c) not extending to 

 infinity, (d) treated by way of Inverse Probability, (e) curves other than 

 " Probabilit}'," (gh) unique and symmetrical. For instance, the law to 

 which Prof. Newcomb reduces his transit-observations (cited below) con- 

 stitutes such a curve, provided that its infinite branches are cut off. 



|| E. g. caused by " Mistakes " which do not obey the typical Law of 

 Error. 



% Laplace, Theorie Analytique^ Supplement 2, sect. 2. Mecanique 

 Celeste, book iii. See ' Observations and Statistics.' 



** For a fuller statement of this reasoning see the writer's Metretike. 



