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There are two ways of treating data which are distributed in this manner: (i) One may actually go over to the logarithms y = log x and proceed as though y were normal or nearly so; in this case m is calculated as the mean of y and ois the standard deviation of y and the usual formulas? m = o, , uJa = o/V2n would apply. (2) Or one may fit the transform by moments on the original data, in which case the values of m and a may be somewhat different and their standard deviations will be determined by other formulas. We propose to discuss briefly some matters, connected with the logarithmic transform, which we believe have had insufficient emphasis. To make the discussion less abstract we shall give numerical illustrations obtained from the distribution of the percentage net debt (state and municipal) of the forty-eight states relative to the wealth of the state as estimated a decade
Wilson et al. (Thu,) studied this question.