442 RESEARCH IN PROTOZOOLOGY 



Mode is the value of that measurement which would occur 

 most frequently if an indefinitely large number of measure- 

 ments were taken. In practice, the mode is a difficult constant 

 to compute, for it should be determined as the modal position 

 of the frequency curve that best fits the observations, rather 

 than as the specific measurement in the series which is most 

 frequent, and this involves the choice of a form of frequency 

 curve, the fitting of such a curve and the determination of its 

 mode. 



2. Constants of variation or dispersion. The common constants 

 of variation are : range, average deviation from the mean value 

 without regard for sign, average positive deviation from the 

 mean value, average negative deviation from the mean value, 

 standard deviation, coefficient of variation, and quartile limits. 



Range is the distance on the scale from the smallest measure- 

 ment to the greatest, and although of interest and significance in a 

 problem, it forms a poor constant by which to judge the variability 

 of the material at hand, since it is dependent on only two of the 

 measurements in the series and is, therefore, an unstable constant. 



Average positive deviation and average negative deviation are, 

 as their titles indicate, the averages of the positive and the nega- 

 tive deviations from the mean, taken separately. 



Standard deviation is the square root of the average squared 

 deviation from the mean. This measure of variation is the one 

 that is in most common use in the field of statistics, although 

 it is difficult for the beginner to see why this should be preferred 

 to average deviation. It will be sufficient to say at this point that 

 the reasons for its adoption in the field of statistics are : 



a. That it is a comparatively stable constant, i.e., relative to 

 other measures of variation, it does not change much from one 

 sample to another when these samples are taken from the same 

 distribution. 



h. It is the measure of variation that is of importance in the 

 method of least squares and in the normal curve of errors. 



c. Tables of distribution of frequency according to this meas- 

 ure of variation have been made up, and are available for use 

 for those problems in which it may be assumed that the material 

 is normally distributed. 



Coefficient of variation is the ratio of the standard deviation to 

 the mean value^ rt)ujtiplied by lOo; that is, it is the variation 



