APPENDIX 



699 



An approximate value for the probable error of a single variate in any 

 population may be easily obtained in the following manner : 

 i . Arrange the variates in the order of magnitude. 



2. Count one fourth of the variates of least measurements and note the 

 measurement of the upper one of these variates. Let u represent this 

 measurement. 



3. Count one fourth of the variates of greatest measurements and note 

 the measurement of the lower of these variates. Let v represent this 

 measurement. 



4. Then - gives the probable error of a single variate. 

 The formula for the probable error in a single variate is 



Es = 0.6745 \, 



where S-*" 2 means the sum of the squares of the deviations from the mean 

 and n is the number of variates. The conception of the probable error of 



Y 



a single variate is of value because it aids in the derivation of the probable 

 error of other important results. The formula for the standard deviation 



is (page 429) A/-- 1 , so that the probable error of a single variate is obtained 



from the standard deviation of the population by multiplying the standard 

 deviation by 0.6745. 



