=averageif( ) with multiple critieria

ONLINE TEST.xlsxI'm trying to get class averages from a list of classes that take a test.

I tried the "averageif( ) which works for getting the class average but I would like to know the Average for the students that are in the class that are either ESL or SPED?

I tried:
=COUNTIFS($B:$B,"Clark",$C:$C,ESL)
=COUNTIFS($B:$B,"Clark",$C:$C,1,$D:$D,">.519")
Which works get to see how many students scored about a STANDARD for passing but my superiors want an overall average. Any help would be appreciated.

Example:

Student Name	Class	Category	Score
John Doe	Science-1	ESL	80%
Jan Rogers	Science-2	SPED	70%