Summarizing data – Problems and solutions.

The collection of datasets in Table 1 is extended, and their more meaningful and, thus, recommended, descriptions based on multiplicative means and multiplicative standard errors or standard deviations are given. Some comparisons appear to be of interest. Necessarily, arithmetic means exceed multiplicative ones, starting from some 15% for small s*s around 1.7 up to more than the sevenfold for s* >7. The lower limits of the 95% ranges, relative to the means, turn increasingly negative with s* growing for the classical version, but remain positive and get smaller for the multiplicative description. Turning to upper limits, the multiplicative limit exceeds the additive one by some 17% for s* = 1.7. With s* = 2.5, the difference is about 25%. For s* = 4.2, there is no difference, and for s* = 7, the additive mean is only half the multiplicative one.