STATISTICAL METHODS IN PROTOZOOLOGY 



443 



measured in terms of standard deviation, stated as percentage 

 of the mean. 



There are two quart He limits, the upper and the lower ; the lower 

 quartile limit is that value below and above which one-fourth 

 and three- fourths respectively of all measurements occur. The 

 upper quartile limit is that value below and above which three- 

 fourths and one- fourth respectively of all measurements occur. 

 It will be seen that the quartile limits are measures of dispersion 

 that are directly associated in idea with the median, and if the 

 median is used as a centering constant, the quartile limits should 

 be used to measure dispersion. 



If the arithmetic mean is used as a centering constant, the 

 dispersion should be measured in terms of standard deviation 

 and coefficient of variation. It is well in any problem to state 

 the range in order that the reader may have some idea as to the 

 extremes of the variation. 



The statistical constants used in connection with the frequency 

 distribution may be found directly from the individual measure- 

 ments by following the definitions given above, but experience 

 with the computation of certain of these constants has enabled 

 the statistician to reduce the arithmetic labor involved to a mini- 

 mum, and it may be useful to indicate the method of determining 

 these constants that has been found to be advantageous. For 

 this purpose we shall compute the values of the arithmetic mean 

 and standard deviation for the frequency distribution given above. 



DETERMINATION OF THE MEIAN AND STANDARD DEVIATION OF THE LENGTH OF 



TROPHOZOITES OF Giavdia Bradypi 



If we use 2 to indicate summation, the following formulae and 

 procedure will be used in determining the mean and standard 

 deviation : 



