STATISTICAL METHODS IN PROTOZOOLOGY 



441 



of thirteen to fourteen microns and that the smallest organism 

 ohserved was ten microns in length and the largest one, sixteen. 

 This simple presentation of the material involves two of the 

 ideas that form the basis of the simple description of any fre- 

 quency distribution ; they are, namely — the concept of measure- 

 ments centering at some point and the concept of deviation or 



/£ 13 14 



LENGTH IN MICRONS 



Fig. 29. — Frequency Distribution of Lengths of Trophozoites of Giardia 



hradypi. 



variation of such measurements from this centering point. Other 

 ideas than these are used in the field of statistics in describing 

 frequency distribution, but these two are fundamental. 



Let us, then, define the statistical constants that are used to 

 present these two ideas : 



I. Centering constants. There are three centering constants in 

 common use ; they are the arithmetic mean, the median, and the 

 mode, and are defined as follows : 



Arithmetic mean or average of a set of measurements is the sum 

 of their values divided by the number of such measurements. 



Median is the value of that measurement above or below which 

 one-half of the observations fall. It should be noted that if the 

 number of measurements is even, the median is not definitely 

 fixed by this definition, but may be any value between those two 

 measurements which are the central ones in the series. It is 

 usual in this case to take the average of the two central values. 



