Conditional Averging of a single cell Across Multiple Worksheets

I am an average or maybe below average Excel user, so please excuse my lack of knowledge with this question. I have been trying to figure this one out for a good while now. Before reading this forum I tried every formula type that the forum said wouldn't work on a three dimensional formula so your help is greatly appreciated.

Basically I need to average cell D3 across multiple worksheets if cell A1 in those worksheets is equal to 1. A list of the names of the worksheets can be found in a worksheet entitled Overall Averages in cells b59:m59. (not the same worksheet the formula in question will be on and not the same one as the A1 and D3 mentioned above are in). Also there may be blanks in the cells to be averaged that should be exluded from the final calculation.

All worksheets above are in the same file. Unfortunately the sheets contain some confidential information and therefore I am unable to upload them.

It sounds easy enough but has been baffling me. Thanks again for all your help.

I tried the formula, but it gave a REF! error. Could this be because the formula did not reference the "Overall Averages" worksheet?

Thanks alot. I just made a list of sheets on the sheet I was working with and it worked like a charm.