270 PROCEEDINGS OF THE AMERICAN ACADEMY. 



n individuals, and let di, (L ... d,^ represent the difference between each 

 number of the series and the mean of all. 

 Then 



0.8453 (c?i + «?2 ••• d„) 



's/n {ii — 1) 



which is the common working formula for probable error,* is a measure 

 of the variability of the given quality in this particular group. 



Or, in symbols, 



T. 0.8453 2 d 



Foe 



^Jn (n — 1) 



where V stands for variability, 2 c? = 6?i + c?2 . . . (f^,, and oc may be read 



" is measured by." This is, appproximately, Galton's Q. 

 Obviously, 



Vcc ^^. (Formula 1.) 



^/n {n — 1) ^ ^ 



In Formula 1, 



Vn {71 - 1) = V»' - n = yjn" (\-]-\ = nJ I --. 



n 



V n 



Consider the expression, — . 



n 



Here 2 c? is the sum of all differences between single numbers of the 



series and the mean of the series. Since these are n in number, — is 



n 



the average deviation of single values from the mean value. 

 Let ad he the symbol for this average deviation. Then, 



V (X. ad — . (Formula 2.) 



V n 



Suppose, however, that the number of cases measured is large ; that 

 is to say, that n is made indefinitely large. As n approaches infinity, 



- approaches 0, and consequently — ^^=^ approaches 1. 

 n 



0^ 



V n 



* See any tex^book treating of such subjects; for example, Merriman ('84), p. 93. 



