phenomenon must make use of it. But in measurements made on a series of distinct individuals the average does not signify the value nearest the truth, and we cannot infer that it is the most significant single representative of the series. The average has this disadvantage, moreover, that the introduction of a few very extraordinary individuals has undue influence on the result. Thus in calculating the average income of American colleges, one institution with an income of $1,200,000 increases the average by an amount ($2,500) equal to the total income of about 5 per cent, of the 'colleges and universities.' The average has indeed been over-rated and over-used, as though it were always the best single representative of a series; whereas there are other representatives which are sometimes superior. Among these is the middle value, which is usually got without much calculation. It
is the value above and below which fifty per cent, of the cases lie. In the case of income of American colleges the middle value is not far from $15,000, while the average is $43,000; the former amount unfortunately gives the truer idea of the usual American college; for about 80 per cent, of the colleges have an income of less than $43,000 Still another representative value is the geometric mean which is especially important in many biologic and economic statistics. The geometric mean is the number corresponding to the average of the logarithms of the individual quantities.
Finally, if there is one representative of a biological series that is more apt to be significant than any other, it is the value that occurs with the greatest frequency or, in other words, the commonest value. Since this value may be said figuratively to be the most fashionable one,
