It seems like nearly every conversation I have about grades eventually turns to online gradebooks. There is a presumption that parents like them...administrators, too...but I have yet to hear from many teachers who appreciate them. This is occasionally due to some sort of mandate that the gradebook be updated a certain number of times per week, but more often than not, it is because of the column at the very end.
It isn't so much a problem with the concept of averaging itself, it's the underlying assumption that the numbers in the boxes represent the only possible data. Once there is some sort of "final" grade showing (which is what parents look for first and last), then any room for professional judgment has gone out the window. All the observations teachers make...all the conversations we have with students...these things don't fit in a traditional gradebook, and yet they deserve consideration.
One district I talked to was looking into ways to not display a summative score with their online grades. Seems like a smart solution to me---I hope they can make the software bend to their will. Better yet, I hope that software makers will catch on and make this a standard option with their offerings.