ListPlot averaging over y-coordinate

Question

I am trying to plot a list of tuples where each “x” coordinate has multiple corresponding “y” values, sort of like {{1, 0.5}, {1, 0.7}, {2, 0.8}, {2, 1.0}…}. I want to create a new list where all the “y” coordinates corresponding to a particular “x” coordinate have been averaged over. So, the previous list would be transformed into {{1, 0.6}, {2, 0.9}…}.

What is the cleanest way I can achieve this? I don’t want to write a for-loop or something like that for such a seemingly-trivial thing.

Answer 1

TDIL that TemporalData[data] does the desired grouping/sorting/averaging when input data contains repeated time stamps.

data = {{1, a}, {1, b}, {5, w}, {2, u}, {5, x}, {5, y}, {5, z}};

TemporalData[data]["Path"]

 {{1, (a + b)/2}, {2, u}, {5, 1/4 (w + x + y + z)}}

Using example data from Bob Hanlon's answer:

SeedRandom[1234];
n = 20;
data = Sort @ Transpose[{RandomInteger[5, n], RandomReal[1, n]}];

simply use {data, TemporalData[data]} in the first argument of ListPlot:

ListPlot[{data, TemporalData[data]}, 
 Joined -> {False, True}, 
 PlotTheme -> "OpenMarkersThick", 
 PlotLegends -> {"data", "means"}]

means = TemporalData[data]["Path"]

{{0, 0.62577}, {1, 0.856999}, {2, 0.684749}, {3, 0.329375},   
 {4, 0.255957}, {5, 0.414358}}

This matches the data set obtained using methods suggested in Bob Hanlon's and upbdqn's answers and Bill's comment:

TemporalData[data]["Path"] ==
 Map[Mean] @ GatherBy[data, First] ==
 Values @ GroupBy[data, First, Mean] ==
 Map[Mean] @ SplitBy[Sort@data, First] ==
 KeyValueMap[List] @ Merge[Mean] @ MapApply[Rule] @ data

True

Answer 2

You can also use GroupBy:

Using the same toy data:

SeedRandom[1234];
n = 20;
data = Sort@Transpose[{RandomInteger[5, n], RandomReal[1, n]}];

Using GroupBy:

gb = GroupBy[data, First, {#[[1, 1]], Mean@#[[All, 2]]} &];
ListPlot[{data, Values[gb]}, Joined -> {False, True}, 
 PlotTheme -> "OpenMarkersThick"]

EDIT

Better answer as per @kglr.

See comment by @kglr (as the larst argument applies to grouped data):

gb = GroupBy[data, First, Mean];
ListPlot[{data, Values[gb]}, Joined -> {False, True}, 
 PlotTheme -> "OpenMarkersThick"]

Answer 3

$Version

(* "13.3.0 for Mac OS X ARM (64-bit) (June 3, 2023)" *)

Clear["Global`*"]

SeedRandom[1234];

n = 20;

data = Sort@Transpose[
   {RandomInteger[5, n], RandomReal[1, n]}]

(* {{0, 0.113153}, {0, 0.233079}, {0, 0.42294}, {0, 0.875912}, {0, 
  0.87966}, {0, 0.884627}, {0, 0.971018}, {1, 0.754358}, {1, 
  0.95964}, {2, 0.397409}, {2, 0.544858}, {2, 0.87433}, {2, 
  0.922399}, {3, 0.329375}, {4, 0.0542848}, {4, 0.254132}, {4, 
  0.459454}, {5, 0.0637313}, {5, 0.331812}, {5, 0.847531}} *)

{#[[1, 1]], Mean[#[[All, 2]]]} & /@ GatherBy[data, First]

(* {{0, 0.62577}, {1, 0.856999}, {2, 0.684749}, {3, 0.329375}, {4, 
  0.255957}, {5, 0.414358}} *)

ListPlot[{data, data2},
 Joined -> {False, True},
 PlotMarkers -> Automatic]