My brain is slowing down this Friday afternoon, and I am having trouble figuring this out. I have 42 GRIDs for a water basin (each representing a year). Each grid contains the attributes for January - December - so 12 attributes with the amount of water received for each month. Is there a way to create one final grid (or maybe one for each month) that contains the 42 year average of water for each month?? Any help or ideas is appreciated. This is what the attribute tables look like...

This will only work is if the ObjectId value identifying each cell is identical across all tables, or there is some other common ID value field the preserves a common CELL ID across all 42 of your GRID tables. If the ObjectID is the only field that uniquely identifies each cell, then it must first be calculated into a Long field that will make its value permanent when you merge the tables. If the ObjectIDs are randomly assigned to any given cell across the tables, they you would first have to come up with a spatial method to assign each cell a specific unique value that is stable across all years and contained in every GRID table to perform any kind of summary by cell.

So first create a LONG field called CELL in every table and calculate the ObjectID of every table into it. Then merge all of the tables into one table. Then use the Summary Statistics tool and use the CELL field as the Unique Case field and each month field as a Summary field with the Mean summary type. All 78,000 cells will have their average created when the CELL field collapses to a single row for each CELL value with 12 columns of Means of the months of the year. This output summary table can then be joined back to the original 42 tables on the CELL field to compare each cell's actual annual month value to the corresponding 42 year mean (average) month column, if you wish to do that.