Average percentage of a subcategory I have a list of numbers of unknown length whose average is x (in fact its 68, but that's not relevant). Some subcategory of that list has an average of y (71) - I don't know how many items are in the subcategory nor what percentage of the list is in the subcategory. Is there any way of working out the average of the numbers not in the subcategory. To give some context, I have attendance figures for a number of students each doing a different number of courses. I have their average attendance and the Maths+English attendance, I'm trying to calculate their "everything but Maths and English" attendance. But the actual situation is a bit of a side issue, more curious as to whether or not it can be done.

No. For example, suppose your list is $(62,71,71)$. This has average $68$.

Case 1: Your "subcategory" just has one entry, $(71)$. This has average $71$. The complement of this is $(62,71)$, which has average $66.5$.

Case 2: Your "subcategory" has two entries, $(71,71)$. This has average $71$. But the complement is $(62)$, which has average $62$.