Averaging Ratios: Characteristics of the Error of Approximation

Ratios are often calculated from experimental and other measurements, but there is some variation in how this is achieved: a ratio of averages (q) or an average of ratios (r) can be calculated depending on the data available. While q is often used as an estimate of r, their expected values are not equal, and their distributions differ from one another and, in some instances, from that of the data from which they are calculated. I give a general expression for the difference between r and q.