Meanquantity

Meanquantity is a statistical concept used to describe the central tendency of a collection of measurements that all represent the same physical quantity and unit. In practice, meanquantity often refers to the arithmetic mean of the measured values, but the term emphasizes that the subjects being averaged are quantities with real-world meaning, not abstract numbers.

For a set q1, q2, ..., qn with the same unit, the meanquantity is (q1 + q2 + ... + qn) / n. If the data represent a population, the population meanquantity mu is (1/N) sum q_i; if they are a sample, the sample meanquantity x̄ is (1/n) sum q_i. When measurements have different units or scales, they should be converted to a common unit before averaging. The meanquantity can be affected by outliers; in such cases, alternatives like the median may be preferred, or robust methods may be used.

When measurements have uncertainties, a weighted meanquantity is often employed: sum (w_i q_i) / sum w_i, with weights w_i typically proportional to 1/σ_i^2. The concept aligns with notions of expectation in probability theory when quantities are treated as random variables with known distributions.

Applications of meanquantity appear in experimental physics, chemistry, engineering, and metrology to summarize repeated measurements such as lengths, voltages, or concentrations. Example: measuring a length yields 2.0 m, 2.5 m, and 2.2 m; the meanquantity is (2.0 + 2.5 + 2.2) / 3 = 2.23 m.