Gathering an average across multiple sheets tied to a specified input

I'm trying to attain overall averages across multiple sheets that are tied to a specific group when chosen.

I'm trying to attain the average "satisfaction" of each specified group that is chosen as a drop down box on the sheets:

And I'd like that average to show up on this sheet:

I'm trying to figure out someway of making a countifs and average function somehow work but I can't seem to wrap my head around it.