array question

[Dr. Harvey Waxman]

=AVERAGE(IF($C$12:$C$7858<=K3,$S$12:$S$7858))
=AVERAGE(IF(($C$12:$C$7858>K3)*($C$12:$C$7858<=K4),$S$12:$S$7858))

These work as expected but I'd like to SUM the entries that satisfy the IF
statement not average them. And the SUMs I'd like are in the C range itself
not the S range.

I can't seem to bend this to do what I want. Should I use some other strategy?
Ideas?

Thanks

Harvey