From a list of (x,y) pairs, generate a new list of (x,ymean) pairs, where ymean is the average of all y's with the same x in the original list

Question

This seems like the sort of thing where Mathematica can give a very simple solution.

I have a list of points {x,y}:

{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 5}}

From this list, I want to generate a new list of pairs {x,ymean}, where ymean is the average of all y's in the original list which were paired to the same value of x:

{{1, 3}, {2, 7/2}, {3, 5}}

What's the simplest, most elegant way to accomplish this in Mathematica?

Something involving GatherBy[list, First], I expect. – May 15 '14 at 18:19 — , May 15 '14 at 18:19

RunnyKine · Accepted Answer · 2014-05-15T18:31:41.803

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Assuming you have your 2D list in a variable named lis, then the following should work:

Mean /@ GatherBy[lis, First]

edited May 15 '14 at 18:31

answered May 15 '14 at 18:21

RunnyKine

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+1 I knew my solution was too complicated... – a06e May 15 '14 at 18:32

score 0 · Answer 2 · answered May 15 '14 at 18:24

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Replace[GatherBy[data, First], d_List :> {First@First@d, Mean[d[[All, 2]]]}, {1}]

where data is the original list of points.

answered May 15 '14 at 18:24

a06e

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From a list of (x,y) pairs, generate a new list of (x,ymean) pairs, where ymean is the average of all y's with the same x in the original list

2 Answers2