There is a quantity (W) that I would like to calculate that is, ultimately, a function of parameters that I can measure directly (a and b), [tex] W = W(a, b) [/tex] But I cannot measure a and b perfectly, there will be some uncertainty in these measurements. This uncertainty will propagate into my calculated value of W. This part, I can do. My problem is that W, itself, will vary slightly over the sample being measured. There is uncertainty, so to speak, in W because of imperfections in the material unrelated to my measurements. Therefore, I can measure a and b once and get values a1 and b1, and calculate W1, with their respective errors. But then I can measure a and b again and get a2, b2, and then calculate a W2 ≠ W1. If I repeat the measures of a and b many times, I will get many values for W. How, then, can I combine all these values for W into a single value and express it with some uncertainty on the overall average W?