Dragging SUM formula

Attached.

So yeah, the dates are listed on worksheet - two times per day for each shift (however there may be more than this, so the number of dates per month can not be relied upon - and if someone does not record the data then of course whole days may be missing). Which makes me wonder if the sumif approach should be used for the weekly data as well as the current method would be susceptible to missing data.

The Sumif would work, just I'm not sure how to set it to go between two dates. Sumproduct would also work I guess? Can something similar be done for average? I'm on excel 2003 and I seem to recall that there is no averageif function.