Without having a clue as to what YOUR definition of "average strength" is here goes:
Logical Chess Move by Move and The Most Instructive Games of Chess Ever Played by Irving Chernev
500 Master Games of Chess by Dr Tartakower & J DuMont
My System by Nimzovitch if you only get one book on this list this is the one!
Practical Chess Endings by Chernev and/or another book by Keres, same title
Catastrophe in the Openings by Yakov Neishtadt
1001 Checkmates by Fred Reinfeld
One or more middlegame books by Fine, Euwe or especially Romanowsky
Many players also like instructional books by Jeremy Silman, but I haven't read any of his works so all I can say is see what other respondents have to say about him and many other authors I haven't read.
Any good chess books for a player considered average strength ?