I have attached two examples of avg of a running sum. The left column uses Pane Down and provides a Avg of the Running Sum for just the values of the current month (starting at zero for each month). The right column is the avg of the Running Sum over all time with the Avg being just for the values consisting of the current month.
This is in version 10 of Tableau Desktop. I didn't know what version you were working with but it could be done in any other version as well.
Left window_avg is just Compute using Pane down
Right window_avg is using the dimensions Month of Order Date (first) and Day of Order Date second.
Set the At the Level fo "Day of Order Date" - since we are computing the avg per day and then set the Restarting every to "Month of Order Date".
I hope this helps out.
Avg Running Sum.twbx 1.9 MB