email@example.com (Julie) writes: >Hello, I was having a bit of trouble understanding something with >weighted averages. Suppose I have the following formula for per-pupil >revenue in a given state: Total Revenue (in a given state)/Average >Daily Attendance (in a given state). Now if I want to find the average >per-pupil revenue across the whole U.S. wouldn't I take the sum of all >total revenues in the U.S.(sum each of the 50 states) and divide that >by the sum of all Average Daily Attendance figures in the U.S. (sum >each of the 50 states)?? Wouldn't this be a weighted average of >per-pupil revenue that is more accurate than taking the sum of all >total revenues and dividing by the number of states?? I'm just having ^^^^^ [should say per-pupil] >problems relating this calculation to the basic weighted average >formula (sum of weight*quanitities/sum of quantities). Is the "weight" ^^^^^^^^^^ [should be weights] >in my calculation the Average Daily Attendance??
Everything you say is correct, apart from the two small mistakes noted above. In your computation, you are starting with the figures for total revenue and for ADA, for each state. So it's clearly right to add total revenues (straightforwardly) and add ADAs (with the caveats you mention later in your message).
But suppose you happened to be given the per-pupil revenues rather than the total revenues. In that case, you might be tempted to add the per-pupil revenues, since that's what you have! And the weighted average formula is telling you that you're not allowed to do that, but must instead recover the total revenues by multiplying each state's per-pupil revenue by its ADA. In the vocabulary of the formula, you weight each state's per-pupil revenue by its population (which is essentially what ADA measures, since for this purpose "population" means "population attending school").
As for computing the average ADA, given the complexities in the formulas used, I'd be inclined to say that there is *no* honest way to average such unlike numbers. Instead you'd have to compute your own ADA figures for each state, using the same formula for each, starting from their raw daily attendance numbers.