What is the recommended statistical approach for describing lognormal data in terms of central tendency?

• A. Use geometric mean and geometric standard deviation.
• B. Use arithmetic mean and standard deviation.
• C. Use median only.
• D. Use mode and range.

Answer: (A)

When data are lognormal, the natural description of central tendency comes from the multiplicative scale because the logs of the data are approximately normally distributed. In that case, the central value on the original scale is best represented by the geometric mean, which equals exp(mean of the log-transformed data). The spread is captured by the geometric standard deviation, which equals exp(standard deviation of the log-transformed data). This pairing reflects how values cluster around a central value in a multiplicative way and aligns with the normal distribution on the log scale. The arithmetic mean can be inflated by the long right tail, and while the median is robust, it does not convey the multiplicative spread as clearly as the geometric standard deviation.