The distance between the centroid of $P$ points and the centroid of a subset of the points - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T04:30:11Z http://mathoverflow.net/feeds/question/105612 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105612/the-distance-between-the-centroid-of-p-points-and-the-centroid-of-a-subset-of-t The distance between the centroid of $P$ points and the centroid of a subset of the points CKura 2012-08-27T09:45:23Z 2012-08-27T15:16:55Z <p>Imagine I have an $(p_1, ..., p_N) \in P$ points, on a two-dimensional plane, patterned in a rectangular or hexagonal lattice arrangement in a circle of radius $R_c$, with a spacing between the points of $r_s$. </p> <p>Let $C_P$ be the centroid of the $P$ points. If I randomly select some subset of $k$ points from $P$, and I compute the centroid of these $k$ points, $C_k$, what is the probability that the distance between $C_p$ and $C_k$ is $\leq D$?</p> <p>Update: I have specified that the $P$ points in the circle are in a rectangular or hexagonal lattice arrangement (whichever is easiest to analyze).</p> http://mathoverflow.net/questions/105612/the-distance-between-the-centroid-of-p-points-and-the-centroid-of-a-subset-of-t/105634#105634 Answer by Igor Rivin for The distance between the centroid of $P$ points and the centroid of a subset of the points Igor Rivin 2012-08-27T15:16:55Z 2012-08-27T15:16:55Z <p>I might not be understanding the question, but the centroid is just the mean of the sample, so for mildly large samples from a mildly large set it will be (bivariate) normally distributed, and all the statistics are easy to compute.</p>