Realistically you would want to use VBA for this ... formula wise you would need to enable Iteration (to permit circular references) and these are Volatile, ie will recalculate whenever excel recalculates be it the result of the value updating or something else so this method is open to error.
In VBA terms, if we assume the cell being altered is A1, the running total to be stored in B1, the count of alterations in C1 then the below VBA might work for you:
Private Sub Worksheet_Change(ByVal Target As Range)
If Target.Address <> "$A$1" Then Exit Sub
Range("B1").Value = Range("B1").Value + Val(Target)
Range("C1").Value = Range("C1").Value + 1
End Sub
To insert the above, right click on the Tab against which the code is to be applied - select View Code and paste above into resulting window, thereafter ensure Macros are Enabled.
Your average calc is thus B1/C1
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