Averaging independent measurements of one true value is optimal under classical statistics

Evidence

A good way to see the unidimensional logic of the mean is via the history of measurement and the role of the mean in that history. Classic measurement theory, e.g., in physics, dealt with situations where scientists were trying to measure descriptive features, such as the position and brightness of stars. Multiple independent physicists would make measurements of the same star. The question was how to aggregate those measurements into one best estimate of the true value. Assuming independent measurements, the classic theorem in statistics states that the mean of those independent measurements was the best estimate of the true (unmeasured) value. — Gary Goertz, Social Science Concepts and Measurement, 1017

Categorization

• XREF: Historical grounding for why the mean is the default in index aggregation — echoes standard error-reduction and measurement-error treatments in statistics.