Geometric mean = nth root of product of n values. Best for compound growth rates.
For investment returns: 20%, 10%, -5%, 15% — geometric mean gives the true annual return.
This calculator is appropriate for any analysis that will be presented, reported, or used to make decisions. Accurate statistical metrics are the foundation of valid conclusions.
Choosing population standard deviation when the data is a sample is the most common statistical error with this type of calculation. Unless your dataset covers every possible member of the group, use sample SD (with n−1 denominator) for valid inference.
A quality engineer analyses the diameter measurements of 25 machined parts: mean 50.02 mm, standard deviation 0.08 mm. With a tolerance of ±0.25 mm, the process is well within specification — and the SD confirms the manufacturing variation is low enough that virtually no parts will fall outside tolerance.
For growth rates, investment returns, and ratios — anything that multiplies rather than adds.
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