10 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



for the more complicated calculations involved in the determination 

 of measures of interrelationship. 



The standard deviation may be calculated by actually obtaining 

 the deviations of the individual measurements from the general average, 

 squaring these deviations, dividing by the number of observations, and 

 extracting the square root of the quotient . Thus if x represents the value 

 of an individual measurement, x the average of all the N measurements 



where a x is to be read "the standard deviation of the measurement x" 

 and 2 denotes the summation of all the squared deviations. Thus in 

 the case of a series of 16 athletes given in our table of data on p. 40 the 

 total weight is 1181.1 kilograms and the average weight 1181.1/16 = 

 73.8 kilograms. The sum of all the daily heat-productions is 30,025 

 calories and the average daily heat-production 1876.6, or in round 

 numbers 1877 calories. The deviation of the individual weights, w, 

 from the average weight, w, and of the individual heat-productions, h, 

 from the average heat-production, h, are given in table 1. 



TABLE 1. Deviations and squares of deviations of body-weight, w, and heat-production, h, 



from their respective averages. 



The standard deviations are therefore given by 



= 2649.09, Z[(h-7i)-]= 961351 



165.5681 = cC <r w = 12.867 

 = 60084.44 = <r,, 2 <r h = 245.12 



The standard deviation furnishes a measure of variation in terms 

 of the unit in which the variable was measured, i.e., in number of 

 heart-beats, in number of respirations per minute, or in number of 

 calories produced per 24 hours. If comparison between the variability 

 of characteristics measured in different working units is to be made, 

 it is necessary to reduce the two standard deviations to a comparable 



