Selecting n data points whose average is nearly as good as the mean

Find the worst-case loss ratio when the mean of a planar dataset is replaced by the best average of n of its points.

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	1	+{
	2	+ "domain": "computer-science",
	3	+ "topics": [
	4	+ "learning-theory",
	5	+ "discrete-geometry"
	6	+ ],
	7	+ "type": "proof",
	8	+ "also": [
	9	+ "construction"
	10	+ ],
	11	+ "source": {
	12	+ "key": "colt",
	13	+ "name": "COLT open problems",
	14	+ "url": "https://proceedings.mlr.press/v291/hanneke25e.html",
	15	+ "id": "v291/hanneke25e",
	16	+ "curator": "Conference on Learning Theory (COLT)",
	17	+ "poser": "Steve Hanneke, Shay Moran, Alexander Shlimovich and Amir Yehudayoff",
	18	+ "status": "open",
	19	+ "as_of": "2026-10-20",
	20	+ "catalog": "0521c19bbd38"
	21	+ }
	22	+}