STATISTICAL METHODS IN PROTOZOOLOGY 



445 



index of variation, it has another value in connection with ma- 

 terial that may be considered to be normally distributed, this value 

 arising from the fact that the standard deviation is one of the 

 important constants in the normal or Gaussian curve of errors. 

 The form of this curve, a knowledge of which is necessary for 

 an appreciation of standard deviation, is indicated in Fig. 30. As 

 will be seen the standard deviation constitutes a unit of measure 

 along the x axis and the area under this curve between any two 

 positions on the x axis (such as A and B) represents the propor- 



scALE or x/a 



Fig. 30. — The Normal Curve. 



tion of cases that would fall within these limits. Since the area 

 under this curve is so frequently needed, tables have been pre- 

 pared which give this area for any positions desired when these 

 positions have been expressed in terms of standard deviation. A 

 brief tabulation - of these areas is given in Table 2 and the table 

 should be read as follows: 



X 



Between the mean and a value of — of unity, thirty-four per 







cent of the area is included and this statement applied to the 



problem at hand indicates that between the mean length, 13.01 



microns, and the length one standard deviation away from this, 



14.06 microns, we would expect to find thirty-four per cent of our 



measurements in case the material is normally distributed. In 



Table 2 the area of the curve has been expressed not only in terms 



of standard deviation but in terms of a unit that is called probable 



'For a complete table of this sort, see Pearl, 1923. 



