Page:Popular Science Monthly Volume 39.djvu/468

 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 comes 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 Statistics, 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 international trade accounts, the miscalculations by individual inquirers, 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 average may indicate two different things. For instance, if one measures Nelson'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 Parisian 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 instances 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 measurement 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 existing. 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 comparisons of the present conditions with the past can be made; and, generally speaking, those who use statistical comparisons covering a period of years should be exceedingly careful that the elements are approximately identical for the various years of the period.

Statistical science improves like all others, and this improvement is doing much to lead empirical statisticians into erroneous