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Default Averageifs & Countifs

I am trying to get the average of a multiple cell range. The criteria range
and sum range are not the same size. Does countifs work the same way
regarding this?
Here is the formula I am trying to rearrange to work.
=AVERAGEIFS(H15:H350,B15:B350, "=01/01/07", B15:B350, "<=01/31/07"). This
one does not give me a true average because I am averaging an average.
=COUNTIFS($C$15:$G$350, J1, $B$15:$B$350, "=01/01/07", $B$15:$B$350,
"<=01/31/07"). I am trying to count a number in the c - g range using a date
criteria.
Can you help?
 
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