STATISTICAL TREATMENT 



235 



where by origin we mean the scale reading corresponding to the zero 

 position for x, and 2 stands for summation, 



Standard deviation = a 



\ 2/ \^f) 



Since these measurements are expressed in terms of 0.5/x, it is necessary 

 to multiply the mean and standard deviation by 0.5 in order to get the 

 values in terms of microns. This process was followed in determining 

 the means and standard deviations given in Table 5. If, as is not 



8 9 I 10 Ti 12 13 14 I 15 ^16 Il7 18 19 | 20 21 I Units of OS Microns 

 -2 -1 Mean +1 +2 +3 Units of 1 cr 



Length 



Fig. 2. — Distribution of length of bodos. 



infrequently the case, a change of one in the x scale corresponds to a 

 change of something other than one in the scale of measurement, adjust- 

 ment for this scale change must be made in the mean and standard 

 deviation. 



Before proceeding to the interpretation of these constants it will be 

 necessary to consider their sampling variation, that is, the extent to which 

 they vary under repeated tests. Study of the theory of errors shows that 

 determination of the arithmetic mean from repeated samples out of the 

 same experience leads to a set of means that are distributed according to 

 a normal probability curve. The standard deviation of this curve is 

 called the standard error of the mean and measures the variation in the 



