Exposure data often follows a lognormal distribution. What do the geometric mean and geometric standard deviation describe, and why are they used?

• A. Geometric mean is the central tendency on the log scale; GSD describes spread; used because data are lognormal.
• B. Geometric mean describes spread; GSD describes central tendency.
• C. Arithmetic mean is the central tendency on the log scale; GSD describes skewness.
• D. Median and variance.

Answer: (A)

When exposure data are lognormal, taking logarithms makes the data resemble a normal distribution, so measures on the log scale are the natural way to describe them. The geometric mean is the antilog of the average of the log-transformed data, so it represents the central tendency on the original scale that corresponds to the typical, multiplicative level of exposure. The geometric standard deviation is the antilog of the standard deviation of the log data, describing spread as a multiplicative factor rather than an additive one. This means most observations fall within a factor of the geometric standard deviation above or below the geometric mean. For example, with a geometric mean of 4 and a geometric standard deviation of 2, typical values lie around 4, within roughly a factor of 2 (between about 2 and 8). We use these because they accurately reflect the multiplicative, skewed nature of lognormal exposure data, avoiding distortions that come from using arithmetic measures.