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When displaying a scatterplot using Graphics, is there a way to use the automatic range for the x and y axes, but force the origin to be centered in the image?

Clarification: I'm trying to force the point (0,0) to be in the center of the graphic, and the axes ranges determined appropriately. i.e. x and y:

PlotRange -> ({-Max[Abs[Data]]), (Max[Abs[Data]])}, {-Max[Abs[Data]]), (Max[Abs[Data]])})

I'm computing a few thousand graphs this way, and computing these ranges literally as above takes a while. I was hoping there were a simple Graphics option. Thanks!

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    $\begingroup$ Please post code. $\endgroup$ – David G. Stork Feb 8 at 1:23
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Alan has the right idea, but if you are using Graphics rather than ListPlot, then it would go like this:

SeedRandom[1]; pts = RandomInteger[100, {50, 2}];
With[{center = Mean /@ Transpose[pts]},
  Graphics[Point[pts], Axes -> True, AxesOrigin -> center]]

plot

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pts = RandomReal[{0, 1}, {50, 2}]
ListPlot[pts, AxesOrigin -> (Mean /@ Transpose@pts)]
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  • $\begingroup$ (+1) you can use Mean@pts instead of Mean /@ Transpose@pts (Mean is Listable). $\endgroup$ – kglr Feb 8 at 7:30
  • $\begingroup$ Thanks! I clarified my question a bit, however, as this was not quite what I meant. $\endgroup$ – user413587 Feb 8 at 15:29
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It seems difficult to use PlotRange->Automatic for this because we don't know the algorithm it uses. The function below accepts a list of points and a number sdevs which gives the number of standard deviations to include each side of the center. The example uses 3. Optional options are passed to ListPlot. Like for PlotRange->Automatic, some points may be outside the range of the plot and not shown.

pts = RandomReal[{0, 1}, {50, 2}];

centeredListPlot[points_, sdevs_, opts___] := 
 Module[{xvals, yvals, cx, cy, center, sx, sy, xRange, yRange},
  xyValues = Transpose@points;
  (* the center *)
  {cx, cy} = Mean /@ xyValues;
  (* sdevs standar deviations from center *)
  {sx, sy} = StandardDeviation /@ xyValues;
  xRange = cx - sdevs {-sx, sx};
  yRange = cy - sdevs {-sy, sy};
  ListPlot[points, PlotRange -> {xRange, yRange} // Evaluate, 
   AxesOrigin -> {cx, cy}, opts]
  ]

centeredListPlot[pts, 2, PlotLabel -> "Centered Plot"]

enter image description here

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I am not sure this is what you want.

SeedRandom@2;
data1 = RandomInteger[{-40, 40}, {50, 2}];
data2 = RandomInteger[{0, 100}, {50, 2}];
data3 = RandomInteger[{-100, 100}, {50, 2}];

data = Join @@ {data1, data2, data3};

max = Max@data;

range = {{-max, max}, {-max, max}};

ListPlot[{data1, data2, data3}, PlotRange -> range, AspectRatio -> 1, 
 PlotLegends -> Automatic]

enter image description here

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