M. Quetelet, who was the first to use statistics in moral directions, explained the principles which ought to guide us in the matter of averages. 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. Quetelet 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 something actually existing, and this is an excellent definition of an average. Tbe measurings and calculations having reference to a number of monuments 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 day, 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 average 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 recently declared that 300 per cent, of the Turks in the city of Washington 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 coeducational 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'