Estimation and the Approximate Geometric Mean

When estimating a value, it is often easier to start with an upper and lower bound on that value. Once you have an upper and lower bound, you can pick a representative point estimate in that interval. The first and most obvious candidate is the (arithmetic) mean of the upper and lower bounds, but this is only valid if the upper and lower bounds are close together, or have the same order of magnitude. If the upper and lower bounds span multiple orders of magnitude, then it is better to use the geometric mean.

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