BoxWhiskerChart can detect and show outliers:

  RandomVariate[NormalDistribution[], 100],

enter image description here

  • What is the precise mathematical criterion used to decide if a point is an outlier?
  • Can this criterion be tweaked?
  • Is this criterion implemented by any documented built-in function?
iqrc = "IQRCoefficient" /. ChartElementData["BoxWhisker", "Options"];


fences = Quartiles[data][[{1, 3}]] + {-1, 1} iqrc InterquartileRange[data]

outliers = Select[Not @* Between[fences]] @ data

{-3.0844, -3.4005}

which matches the vertical coordinates of outlier glyphs:

Cases[BoxWhiskerChart[data, "Outliers", PerformanceGoal -> "Speed"], 
 Inset[_, {_, a_}] :> a, All]

{-3.0844, -3.4005}

  • $\begingroup$ Does ChartElementData[..., "Options"] appear anywhere within the documentation? I cannot find it (though I did find it in other SE answers). $\endgroup$ – Szabolcs Jan 15 '20 at 8:25
  • 1
    $\begingroup$ @Szabolcs, afaik it does not appear in documentation. I think I bumped into it using the spelunking trick: ClearAttributes[ChartElementData, {Protected, ReadProtected}]; ?? ChartElementData $\endgroup$ – kglr Jan 15 '20 at 10:34
  • 1
    $\begingroup$ I found one example in BarChart >> Options >> ChartElementFunction >> last example: ChartElementData["GradientRectangle", "Options"] $\endgroup$ – kglr Jan 15 '20 at 10:39

It is actually in the help documentation as the last item. Outliers are 1.5 InterQuartileRanges (IQR) away from the nearest quartile and Far Outliers are 3 IQR distant.

 Documentation Snippet from Properties & Relations

  • $\begingroup$ Indeed! It's under Properties and Relations. I found that, deleted the question, then undeleted when someone mentioned that they were just about to post an answer. $\endgroup$ – Szabolcs Jan 15 '20 at 7:38

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