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In a previously posted question VLC used the element specification

{"MedianMarker", filledCircle[10], Black}

in a box and whisker chart, where

filledCircle[size_] := Graphics[{Black, Disk[]}, ImageSize -> size]

VLC was dissatisfied with the way the his filled circles were displayed in the resulting chart. Two answers were offered and there was some lively discussion in the comments.

Strangely there was an elephant in the post and nobody noticed it. According to the Mathematica documentation on BoxWhiskerChart, the second element in a MedianMarker specification is a number specifying the width of the horizontal line used to draw the median marker. There is no indication that a function application evaluating to a graphics object is acceptable.

Thus my questions: Why does what VLC did work at all? Has he discovered a undocumented feature?

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I don't think it is undocumented on purpose... poorly documented maybe. PlotMarkers also allows you to use custom graphics instead of text based markers, so by extension, it was equally probable that a different *Marker also accepts graphics objects. I've never used BoxWhiskerChart, but if I had to, I would've thought of trying a Graphics object, even if the docs didn't suggest it –  rm -rf Nov 1 '12 at 13:29
    
It's not entirely undocumented; there's an example using it in Scope > Elements –  Brett Champion Nov 1 '12 at 13:57
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@BrettChampion Not really the same thing I'm bringing up here -- that shows a text character can be used not a graphics object. –  m_goldberg Nov 1 '12 at 14:57
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@m_goldberg Anyplace you can use a text marker in a graphic, you can generally use anything. –  Brett Champion Nov 1 '12 at 16:16
    
@BrettChampion That's an interesting observation. I'll keep it in mind. –  m_goldberg Nov 1 '12 at 20:30
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1 Answer

up vote 1 down vote accepted

The documentation for the different markers explicitly states width for many markers...

      {"Fences", width, style}        width and style of fences
      {"MeanDiamond", width, style}   width and style of mean confidence interval
      {"MeanMarker", width, style}    width and style of mean marker line
      {"MedianNotch", width, style}   width and style of median confidence interval
      {"MedianMarker", width, style}  width and style of median marker line
      {"Outliers", marker, style}     marker symbol and style for outliers
      {"FarOutliers", marker, style}  marker symbol and style for far outliers
      {"Whiskers", style}             style for whiskers

...however, as Brett has pointed out, one of the documentation examples (Scope > Elements) shows how to pass a textual marker to an element that (according to the docs) should only accept width & style values:

Table[BoxWhiskerChart[data, {{"MeanMarker", m, Black}}],
  {m, {"\[EmptySmallCircle]", "\[CircleTimes]", "\[Times]"}}]

Mathematica graphics

So it is reasonable to assume that other markers work the same way and accept textual or graphical symbols. As a matter of fact, anything can be used, even images, though if the second argument is non-numerical (i.e. not the width value), the third style specification cannot be omitted. As rm -rf put it in the comments:

"I don't think it is undocumented on purpose... poorly documented maybe. PlotMarkers also allows you to use custom graphics instead of text based markers, so by extension, it was equally probable that a different *Marker also accepts graphics objects." (rm -rf)

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