34 Mr. F. Gal ton on Statistics by Inter comparison, 



The process of obtaining mean values &c. now consists in 

 measuring each individual with a standard that bears a scale of 

 equal divisions, and afterwards in performing certain arithmetical 

 operations upon the mass of figures derived from these numerous 

 measurements. I wish to point out that, in order to procure a 

 specimen having, in one sense, the mean value of the quality 

 we are investigating, we do not require any one of the appli- 

 ances just mentioned : that is, we do not require (1) indepen- 

 dent measurements, nor (2) arithmetical operations ; we are (3) 

 able to dispense with standards of reference, in the common ac- 

 ceptation of the phrase, being able to create and afterwards indi- 

 rectly to define them ; and (4) it will be explained how a rough di- 

 vision of our standard into a scale of degrees may not unfrequently 

 be effected. Therefore it is theoretically possible, in a great 

 degree, to replace the ordinary process of obtaining statistics by 

 another, much simpler in conception, more convenient in certain 

 cases, and of incomparably wider applicability. 



Nothing more is required for the due performance of this 

 process than to be able to say which of two objects, placed side 

 by side, or known by description, has the larger share of the 

 quality we are dealing with. Whenever we possess this power 

 of discrimination, it is clear that we can marshal a group of 

 objects in the order in which they severally possess that quality. 

 For example, if we are inquiring into the statistics of height, we 

 can marshal a number of men in the order of their several 

 heights. This I suppose to be effected wholly by intercompa- 

 rison, without the aid of any external standard. The object then 

 found to occupy the middle position of the series must possess 

 the quality in such a degree that the number of objects in the 

 series that have more of it is equal to that of those that have 

 less of it. In other words, it represents the mean value of 

 the series in at least one of the many senses in which that term 

 may be used. Recurring to the previous illustration, in order 

 to learn the mean height of the men, we have only to select the 

 middlemost one and measure him ; or if no standard of feet and 

 inches is obtainable, we must describe his height with reference 

 to numerous familiar objects, so as to preserve for ourselves and 

 to convey to strangers as just an idea of it as we can. Similarly 

 the mean speed of a number of horses would be that of the horse 

 which was middlemost in the running. 



If we proceed a step further and desire to compare the mean 

 height of two populations, we have simply to compare the repre- 

 sentative man contributed by each of them. Similarly, if we 

 wish to compare the performances of boys in corresponding 

 classes of different schools, we need only compare together the 

 middle boys in each of those classes. 



