Try this amendment to your formula:

=AVERAGE(IF((Sheet1!A$2:A$5310=Sheet2!A2)*(Sheet1 !B$2:B$5310<=Sheet2!B2),Sheet1!I$2:I$5310))

As this is an array formula then once you have typed it in (or
subsequently edit it) you must use CTR-SHIFT-ENTER instead of just
ENTER. If you do this correctly, Excel will wrap curly braces { }
around the formula - you must not type these yourself.

Hope this helps.

Pete

Jason wrote:
I am trying to average time for multiple entries over a year. I have about
10,000 records with the date and a total time. On my next sheet I have the
start date and end date for each week of that year columns A&B respectivly.
The formula below returns a result but it is wrong. I ran an average for the
first week to conform it and it is off by more than 20 seconds. Can anyone
show me what I did wrong. Thank you

{=AVERAGE(IF(Sheet1!A$2:A$5310=Sheet2!A2,IF(Sheet 1!B$2:B$5310<=Sheet2!B2,Sheet1!I$2:I$5310)))}