BREWSTER, — RANGE OF VARIABILITY. 271 



If, then, n be taken sullicieutly large, 



Fa ad. (Formula 3.) 



Even if n is not large, Formula 3 may usually be employed in practice. 

 For in any single investigation n is likely to be constant, — when, as 

 will often be the case, different qualities of the same individuals are to be 

 compared it is necessarily so, — but the introduction of a constant factor 

 will not affect the correctness of the formula. 



Practically, a d may be found accurately enough without the hibor of 

 subtracting each quantity from the mean. 



Let 



a + -»---- a ■\- d, a -\- c, a -\- b, a — b, a — c, a — d • • • • a — - 



be a series of quantities, n in number, distributed according to the law of 

 probability. The mean is evidently a, and the differences between the 

 several quantities and the mean are 



-, d, c,b,b, c, d, . 



"^ +d+c + b + b + c + d.... + l 

 .*. ad^ — 



n 

 2b+ 2c + 2d .... + n 



n 



(Formula 4.) 



Or, again, 



« + y a -\- d, a -\- c, a -\- b. n — b, a — c, a — d, « — k* 



being the series of n measurements as before, the sum of all terms greater 

 than the mean is 



(« + • • • • + (« + rf) + (a + c) + (a + 5), 



and of these the mean is 





n 

 2 



