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A short explanation of the question: Sometimes it is needed to use a formula as criteria instead of a given criteria. For example if you need to find the sum of numbers that are above or below the average in the range.
For both COUNTIF and SUMIF formulas, the way to use another formula for criteria is the following (pretext: range of numbers is A1:A15):
=countif(A1:A15;">"&average(A1:A15))
or
=sumif(A1:A15;">"&average(A1:A15);A1:A15)
And for the case that any number should be exactly the same as the average, use the "=" sign after the ">" or "<" sign.
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