What is a geometric mean?
The geometric mean is a measure of central tendency, just like a median. It is different than the traditional mean (which we sometimes call the arithmetic mean) because it uses multiplication rather than addition to summarize data values. The geometric mean is a useful summary when we expect that changes in the data occur in a relative fashion. Here are some examples where we would expect relative changes: • Filters will trap dusts in an amount relative to the amount of air flowing through them. • Adjustments in salary are often a percentage amount. • Kidney enzymes usually metabolize drugs in proportion to the amount of drug in the blood. Geometric means are often useful summaries for highly skewed data. They are also natural for summarizing ratios. Don’t use a geometric mean, though, if you have any negative or zero values in your data. Consider a dataset looking at an index representing the ability of an infant to metabolize certain types of drugs. We measured infants at two weeks o
