Conditional Sum (Excel 2000-2004)

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I have created a SUMIF report that sums several sets of dollar amounts associated with a location on another sheet. The SUMIF(Sheet!A5:A628, A4,Sheet!H5:628) works fine as long as there is an exact 1:1 match of the criteria value to the value on the summary report sheet range. However, I need to be able to set a value like (>=704 and < 705) for the criteria, as some of the referred values lie in the range 704.0-704.9. Is it possible to use a condition like this in a SUMIF function? I've tried several variations, but cannot seem to get it to work.
Thanks!

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You could do something like this:

=SUMIF(Sheet!A5:A628, ">=704",Sheet!H5:H628)-SUMIF(Sheet!A5:A628, ">=705",Sheet!H5:H628)

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Thanks Legare, that does exactly what I wanted!

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