Please try something like:
=query({Sheet1!A1:B10;Sheet2!A1:B10},"select Col1, Avg(Col2), count(Col1) where Col1 is not NULL group by Col1 label Col1 'name', count(Col1) 'number of times referenced?', Avg(Col2) 'average'")
Adjust ranges to suit those you did not mention.
For your sample not necessary but you might want to insert order by Col1 asc
before the first label
.