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	"review": true,
23	"approval": "first-time"
24	}