444 RESEARCH IN PROTOZOOLOGY 



N = 2f = 100 2'j-/ = loi I^x^f = 213 



Xt-f loi 

 A^ 100 



V2 =z——L — — ^=2.13 

 A^ 100 '^ 



2 



1. 0201 



Standard deviation = o = \^Jh = 1-0535 



Mean = origin + *'i = 12 + i.oi = 13.01 



While the above computation form is self-explanatory, it will 

 perhaps be well to call attention to one or two points. The scale 

 labeled .v in the form above is arbitrary as to the choice of its 

 origin. It really constitutes a new scale of length in microns with 

 a O-point at twelve microns and with graduations of one micron 

 above and below this O-point. In certain cases the unit choaen 

 on the A'-scale is not the exact unit on the original scale of 

 measurement, but is some multiple of it. The reason for intro- 

 ducing this new scale is to cut down the arithmetic involved, and 

 its origin and the size of its units are chosen so as to keep the 

 X values as low as possible. In the case where the unit on the 

 X scale is some multiple of the unit on the actual scale of length, 

 it is necessary to change the mean and standard deviation back to 

 the units of the original scale. 



The terms v^ and V2 are called relative moments and together 



with higher moments such as v^ = ^ , v^ = ./ , etc., are com- 

 mon in statistical computation. The higher moments are used for 

 the determination of statistical constants of more complex char- 

 acter, — such as the mode, skewness, etc., the determination of 

 which will not be considered in this article but may be found in any 

 text in the statistical method. 



The arithmetic average is used so commonly as a centering 

 point that it is perhaps unnecessary to discuss its properties, but 

 it may be advisable to consider the possible interpretations of 

 the standard deviation. By definition, standard deviation is the 

 root mean squared deviation from the arithmetic mean, and may 

 be used directly as an index of variation, the value of which 

 will increase with experience in its use. Aside from its use as an 



