My worksheet has a tab for each quarter, with data on each tab as in
the example below:

REGION SCORE
Asia 3.4
Asia
Asia 4.0
EMEA
EMEA 2.7
NA 3.9
NA
etc.

In other words, there are multiple regions, and each row may or may not
have an associated score.

On each tab, I've successfully averaged the scores by region using the
following formula:
{=AVERAGE(IF((A$4:A$92="EMEA")*ISNUMBER(L$4:L$92), L$4:L$92))}

However, I need to insert a summary tab which averages the scores by
region across the quarterly tabs. I've tried a couple variations on
the above formula but I don't really know how to adapt it to perform
this calculation.

Any advice would be greatly appreciated!!