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the log transformation can be used to make highly skewed distributions less skewed this can be valuable both from making patterns in the data more interpretable and for helping to meet the assumptions of inferential statistics this figure plots the brain weight of animals as a function of their body weight not only is the distribution very skewed but the pattern is also very hard to discern in this figure the log of brain weight is plotted as a function of the log of body weight this pattern is much more interpretable the comparison of the means of log transform data is actually a comparison of geometric means this occurs because as shown next the antilog of the arithmetic mean of log transformed values is the geometric mean this table shows the numbers 110 and 110 the arithmetic mean of the three logs is the quantity 0 plus 1 plus 2 divided by 3 which equals 1 the geometric mean is the cubed root of the product of the three numbers which is equal to the cubed root of 1,000 which equal
