I am trying to find the average of these test scores:
100 (this one is worth 25%, however)
I don't know how to do this because of the special one
No. If the last is worth 0.0625 and the others are worth four times as much, the others would be worth 4(0.0625)= 0.25, not 0.3125. And .25+ .25+ .25+ .0625 does not add up to 100%. I think you mistakenly took 1/4 of 1/4 to get 1/16 and the divided the remaining 15/16 by 3 to get 5/16 for each of the original three. You mistake was treating the first three as 1/4 each when you knew from the start that you were NOT dividing these equally.
Call the value of each of the first three "a" the last is worth "a/4". So we must have a+ a+ a+ a/4= 3a+ a/4= (12a+ a)/4= 13a/4= 1.00 so a= 4/13. each of the first tests is worth 4/13 and the last text is worth 1/4 of that, 1/13.