4,-2 THE POPULAR SCIENCE MONTHLY. 



statistics may be ; and to show, further, that the value of statistics 

 depends upon not only the integrity of their basis, but also on 

 their intelligent and honest analysis. 



Another line of fallacies conies from the misuse of averages. 

 Mr. W. L. Sargant, in his Essays published in London in 1870, 

 has an exceedingly interesting chapter entitled The Lies of Statis- 

 tics, and I am indebted to him to some extent for an illustration 

 as to averages. The frequent fallacies in the practice of striking 

 averages add greatly to the disturbing influences resulting from 

 inaccurate enumerations, the perplexity and differences in inter- 

 national trade accounts, the miscalculations by individual inquir- 

 ers, and the inadequate consideration of all the elements of tabular 

 statements. M. Quetelet explained the principle which ought to 

 guide us in the matter of averages. He pointed out that an aver- 

 age may indicate two different things. For instance, if one meas- 

 ures Nt-lson's Monument ten times, and always with a slightly 

 different result, and then adds the measurements together and 

 divides the sum by ten, the quotient is an average or mean. So 

 one may accurately measure the Duke of York's Pillar, the Pa- 

 risian obelisk, and the Column Vendome, add the measurements 

 together and divide the sum by three, and declare the quotient to 

 be the average or mean height of these three monuments. M. 

 Quetelet contended, and properly, that the results in the two in- 

 stances are of such different significance as to require two separate 

 names. He would limit the term "average or mean" to cases 

 represented by the first illustration the repeated measurement 

 of one monument and he would apply the term " arithmetical 

 mean " to cases represented by the second illustration the meas- 

 urement of several monuments. The repeated measurement of 

 one monument results in a mean approximation to something 

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

 The measurements 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 exist- 

 ing. It is through a misunderstanding of these elements that we 

 have so many misleading statements of statistics relating to wages 

 and prices. The development of wage statistics has kept pace 

 with all statistical methods. The great trouble is that, on account 

 of faulty presentations in the past, no very satisfactory compari- 

 sons of the present conditions with the past can be made; and, 

 generally speaking, those who use statistical comparisons cover- 

 ing a period of years should be exceedingly careful that the ele- 

 ments are approximately identical for the various years of the 

 period. 



Statistical science improves like all others, and this improve- 

 ment is doing much to lead empirical statisticians into erroneous 



