446 Averages. [CHAP. xvm. 



mean, though such employment would be tedious, owing 

 to the difficulty of calculation. The maximum ordinate 

 clearly would not answer, since it would generally (v. the 

 diagram on p. 443) refer us back again to the average 

 already obtained, and therefore give no information. 



The only point here about which any doubt could arise 

 concerns what is called in algebra the sign of the errors. 

 Two equal and opposite errors, added algebraically, would 

 cancel each other. But when, as here, we are regarding 

 the errors as substantive quantities, to be considered on 

 their own account, we attend only to their real magnitude, 

 and then these equal and opposite errors are to be put upon 

 exactly the same footing. 



10. Of the various means already discussed, two, as 

 just remarked, are in common use. One of these is fa 

 miliarly known, in astronomical and other calculations, as 

 the Mean Error, and is so absolutely an application of the 

 same principle of the arithmetical mean to the errors, that 

 has been already applied to the original magnitudes, that it 

 needs no further explanation. Thus in the example in the 

 last section the mean of the heights was 66 inches, the 

 mean of the errors was 3 T 3 g- inches. 



The other is the Median, though here it is always known 

 under another name, i.e. as the Probable Error ; a tech 

 nical and decidedly misleading term. It is briefly defined 

 as that error which we are as likely to exceed as to fall 

 short of: otherwise phrased, if we were to arrange all the 

 errors in the order of their magnitude, it corresponds to that 

 one of them which just bisects the row. It is therefore the 

 median error : or, if we arrange all the magnitudes in suc 

 cessive order, and divide them into four equally numerous 

 classes, what Mr Galton calls quartiles, the first and 

 third of the consequent divisions will mark the limits of 



