io6 POPULAR SCIENCE MONTHLY. 



M. Quetelet, who was the first to use statistics in moral directions, 

 explained the principles which ought to guide us in the matter of aver- 

 ages. He pointed out that an average may indicate two different 

 things. For instance, one measures Nelson's monument ten times, and 

 always with a slightly different result, and then adds the measurements 

 together and divides the same by ten, the quotient, it is alleged, being 

 an average or mean. So one may accurately measure the Duke of 

 York's Pillar, the Parisian Obelisk and the Column Vendome, add the 

 measurements together, divide the sum by three, and declare the 

 quotient to be the average or mean height of those monuments. Quete- 

 let contended, and very properly, that the results in the two instances 

 are of such different significance as to require two separate names. 

 He would limit the average or mean to cases represented by the first 

 illustration — repeated measurements of one monument — and he would 

 apply the term 'arithmetical mean'' to cases represented by the second 

 illustration — the measurement of several monuments. The repeated 

 measurings of one monument result in a mean approximation to some- 

 thing actually existing, and this is an excellent definition of an average. 

 Tbe measurings and calculations having reference to a number of monu- 

 ments result in no knowledge of anything existing; they simply and 

 only indicate a relation among things actually existing. 



This difficulty often appears in reporting average wages. Take, 

 for instance, a works employing 20 men at $1 per day, 40 men at $2 

 per clay, and 60 men at $3 per day. The ordinary bookkeeper in a 

 counting room would add these rates together — $1, $2 and $3 — making 

 a total of $6 as the result of the different rates. He would divide 6 

 by 3, the number of rates, and declare that the average wages in his 

 works was $2 per day. This is an arithmetical mean. The true aver- 

 age is to be obtained by a more elaborate calculation. Twenty men 

 at $1 earn $20, 40 men at $2 earn $80 and 60 men at $3 earn $180 per 

 day. Thus, 120 men earn $280 per day. Dividing $280 by 120, we 

 have the true average, which is $2.33 instead of $2, the arithmetical 

 mean. So also there are many fallacious calculations drawn from the 

 use of percentages. 



Some amusing incidents happen from this method. A writer re- 

 cently declared that 300 per cent, of the Turks in the city of Washing- 

 ton were criminals. On investigation it appeared that there was one 

 Turk in the city, and he had been convicted three times. So of the 

 young student who took for his thesis the assertion that women in co- 

 educational colleges more frequently married during their college course 

 than men in the same institution. He found a college in which there 

 were 100 men and 2 women. One of the men married one of the 

 women. Hence he sustained his conclusion that 1 per cent, of the men 

 married, while 50 per cent, of the women married. Thorold Rogers' 



