92 PROCEEDING.* OF THE ANATOMICAL AM) A M IIR()l'()l,(KiICAL 



In the following table column L contains head lengths and 

 column B head breadths arranged in series ; columns contain 

 frequencies of the L's and B's ; columns ,K contain distances from 

 an arbitrary point near the mean (in case of the lengths 195 and 

 of the breadths 155) ; columns z< contain first moments about the 

 arbitrary points ; and columns c.r the second moments about these 

 points. 



The results of the calculations in the table enable us to get very 

 easily the mean values and the standard deviations of the lengths 

 and breadths. Since ^i (for the lengths) is the arm of the first 

 moment about 195, it represents the distance of 195 from the mean, 

 and the mean is found by adding p.i (with its proper sign) to 195 ; so 

 with fii for the breadths. 



To find the standard deviation, we have to find p. 2 about the 

 mean by the equation given above, namely : 



^2 = Pi ~ /V 



For lengths = 32-863 - (1-0165) 2 

 = 32-863 - 1-033 

 = 31-830 

 Now fjL 2 = o' 2 



Therefore a = v/3 1-830 = 5-642, is the standard deviation of 

 the head lengths. 



For breadths f, 2 = 28-24 - (2O879) 2 



= 23-881 



(T -=- \/23 T 881 = 4-887, is the standard deviation of 

 the head breadths. 



To TEST WHETHER THE DIFFERENCE BETWEEN Two MEANS is 



SIGNIFICANT. 



Let us assume that we have calculated the average stature of 

 two groups of people, and that we find there is a small difference 

 between the two averages. We have no right to assume that the 

 difference between the averages of the two groups indicates a real 

 difference in the class or race from which they are taken till we have 

 calculated the greatest difference that is practically possible between 



