You can't do an average of an average - it's an invalid statistic.  I assume  that you're doing the averages by group for what you have.  What you need to do to get the final average is run the average as a Grand Total instead of by group.  This will sum the scores for all records and divide by the total number of scores on the report.

I would weight the scores, then average, like if new then score x2 and if old scorex1 or something