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 problems relating this calculation to the basic weighted average formula (sum of weight*quanitities/sum of quantities). Is the "weight" in my calculation the Average Daily Attendance??
Similarly, suppose the formula for Average Daily Attendance (for a given state)= aggregate number of days pupils (in a given state) attend class/total number of days in school year (for a given state). If I want a national average for average daily attendance, rather than summing the Average Daily Attendance for each state and dividing by 50, would I sum the aggregate number of days pupils attend class in each state and divide by the cumulative number of days in a school year for all states? Is this correct and would this be considered a weighted average?? Would the weight be the total number of days in a school year (for a given state)?? Again, I am having problems seeing how the basic weighted average formula applies to this calculation.
Another problem I anticipate having is that not all states use the above formula for average daily attendance (i.e. some have complex formulas incorporating summer school students, actual number of hours students attended class rather than number of days, etc.) In this case, would simply taking the sum of Average Daily Attendance and dividing by number of states be the best way to calculate Average Daily Attendance or is there another weighted mean that is preferable?? Thanks for any insight!!!