Antibody titres against a virus are measured in 200 vaccinated children and the values show a log-normal distribution. Which measure of central tendency is most appropriate for summarising these titres?

• A Arithmetic mean
• B Mode
• C Median
• D Geometric mean ✓

Explanation

Titres that rise in multiplicative steps follow a log-normal distribution, and the geometric mean, calculated as the antilog of the mean of the logarithms of the values, is the conventional summary for such data. It is also the standard measure for averaging ratios and rates of growth. The arithmetic mean is pulled upward by the skew of a log-normal distribution, which is precisely why it is avoided for titre data.

Reference: Mahajan's Methods in Biostatistics for Medical Students and Research Workers, 10th ed.

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