THE MEASUREMENT OF VARIATION. 23 



deviations from the theoretical values were of course 

 greater, but these differences almost completely neu- 

 tralise each other in the general mean. Indeed the 

 correspondence is extraordinarily close, considering the 



verv mixed nature of the faculties measured, viz.. three 

 a // 



linear measurements, one of weight, one of capacity, 

 two of strength, one of vision, and one of swiftness. 

 The next series of values is that obtained by Professor 

 Weldon for 400 shrimps. It is given to show that in 

 the case of a comparatively small number of observa- 

 tions, the correspondence between fact and theory may 

 be very close indeed. Finally, in the bottom line of the 

 table are given the values obtained by the author for 

 9850 measurements on the body length of sea-urchin 

 larvae. Here the correspondence is closer even than in 

 the anthropometric measurements, the average differ- 

 ence being only .014, as against .0175. 



In order to express the variability of a characteristic, 

 we are by no means limited to the method of determin- 

 ing the probable error. A much older method is that of 

 the arithmetic mean error, or average deviation. This 

 value consists of the mean of all the deviations, both 

 positive and negative, from the general mean. For in- 

 stance, to determine the arithmetic mean error of the 

 following series of 16 



7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13. 



figures, one calculates the general mean, viz., 10, and 

 determines their deviations from it. These are 



3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3. 

 Added together these equal 20, so that the arithmetic 



20 



mean error is ^-^ = 1.25. In practice, it is sometimes 



lo 



