404 



L{fe and Letters of Franch Gulton 

 Diagi'am,from the tabular i"</h<'s. 



0" — Hf— lV—W—Vf-z.»f^l(f— 70*— Vf- 90'— 'J* 



The continuous line is the nonuul curve with p.e. - Xl . 



The broken line is drawn from the observations. 



The lines connecting them show the differences between the observed and the normal 



According to this method of dealing with tlie matter the "Vox populi" wtis 

 only wrong nme jxjunds (1207 against 1 198), or 8 per cent. Galton considers 

 that the judgments were not distributed normally and that negative erroi-s 

 were magnified and positive errors minimised by the competitors. But what 

 if Galton be not fitting the best curve to his data? It is not hard to show 

 that the judgment of the middlemost man is not the best median — para- 

 doxical as it may seem! Almost any pair of symmetrical percentiles gives 

 a result with less probable error. For example, the median of the quartiles 

 i (1162 -I- 123G) is 1199, only 1 lb. out. Other medians are: 



aO°and80° 

 1195 lbs. 



80° and 70° 

 1202 lbs. 



35° and 65° 

 1203 lbs. 



40° and 60° 

 1203 lbs. 



— all better than the middlemost value. 



Again the 25° and 75° are far from being the best percentiles to obtain 

 the "probable error" from, i.e. the quartile does not give the quartile best, 

 strange as that may appear. If we calculate the quartile from the 15' and 

 85'' percentiles it is 4 (73 + 55) x l/r54 = 4r5 and this is nearly the best 

 position for detennining its value, on the assumption of a normal distribution'. 

 With median at 1199 and quartile or probable error 4r5, a much more 

 reasonable distribution is found, and there is far less need to assume as Galton 

 did that the individual judgments are abnormally distributed; it is no| 

 longer tnie to say that errors in defect have been exaggerated, although 

 errors in excess are still minimised. Whether the "fit" is a reasonable one it] 

 is not possible to determine when the data are thus given in percentiles. 

 I have dwelt on the matter, because Galton's use of the values at 25°, 50° and 

 75° to determine the median and quartiles is not the best, and may lead, as] 



' Unfortunately the [KTcentile method of tabulation does not permit of very ready deter^ ' 

 mination of the mean and Ntiiiidard deviation and so of getting the best normal distriimtion, ! 

 But I find aft«'r some lalxjur : mean 1197, standard deviation 6 1 "^95, leading to a [)rol)al)le error \ 

 or quartile value of 4 1 '75. Thes*! give a far Ixitter fit than Gallon's median and quartile values. 

 I have inaeried a column on tlie right of the table giving my results. 



