Which statistics are appropriate for describing lognormal exposure data?

• A. Geometric mean and geometric standard deviation
• B. Arithmetic mean and standard deviation
• C. Median and interquartile range
• D. Mode and range

Answer: (A)

When exposure data are lognormal, values are multiplicative and the distribution is right-skewed, so summaries on a multiplicative scale are more informative. Taking a log transform converts the data to a normal distribution, and the corresponding descriptive statistics on the original scale become geometric statistics.

Geometric mean and geometric standard deviation are the best choices here. The geometric mean is the exponent of the mean of the log-transformed data, and it equals the median of the original lognormal distribution, providing a central tendency measure that isn’t pulled upward by extreme high values. The geometric standard deviation is the exponent of the standard deviation of the log-transformed data and describes spread on a multiplicative scale, capturing how much values vary in a factor-like way.

Arithmetic mean and standard deviation can be distorted by the heavy right tail of a lognormal distribution, giving a misleading sense of the typical exposure and variability. The median with interquartile range is robust and informative on the original scale but does not quantify multiplicative variability as directly as the geometric summary. Mode and range are less informative for characterizing the central tendency and overall spread of lognormal data.

So, geometric mean and geometric standard deviation best describe lognormal exposure data.