Is it possible to build a compact proof of the sum of all even numbers of a dataset?
Let's ignore the zk requirement. And focus on compactness. If we have a merkel tree and I swap just one element at random so one of the hashes is invalid and doesn't match the data. We get a merkel tree with almost all valid hashes. Someone would have to verify all of them to catch the foegery. If you only sampled a few paths you would gain little confidence.
Any extra calculations you require on the tree could be done onhe forged version. I'm afraid your request is impossible.