Using a BoxWhiskerChart as a plot marker in ListPlot

Question

I want to plot the means of several data sets, but instead of using a point I would like to use a box-and-whisker plot to represent the full data set. Here is what I mean (with some toy data):

a = {1.7610325845854935, 1.4482381483503182, 1.262594767165387, 2.2720460660207409};
b = {2.1844741151332943, 3.5175853047673318, 3.5245233201347768, 2.0819498353445609};
c = {1.3755036246747516, 1.6169073661736904, 2.3472569940481094, 2.9457474653314475};
dat = {a, b, c};
ListPlot[Table[Mean[dat[[i]]], {i, Length[dat]}], 
    PlotStyle -> PointSize -> Large, PlotRange -> Full]

I would like to set the PlotMarkers in a way that the first marker is a box-and-whisker of a, the second a box-and-whisker plot of b, and so on.

Thank you in advance for any help you can offer!

Answer 1

Using Show[] to combine your graph with the BoxWhiskerChart[] (update: incorporated comment)

a = {1.7610325845854935, 1.4482381483503182, 1.262594767165387, 2.2720460660207409};
b = {2.1844741151332943, 3.5175853047673318, 3.5245233201347768, 2.0819498353445609};
c = {1.3755036246747516, 1.6169073661736904, 2.3472569940481094, 2.9457474653314475};
dat = {a, b, c};

Show[
 BoxWhiskerChart[dat, {"Mean", {"MedianMarker", None}}],
 ListLinePlot[Mean /@ dat, PlotRange -> Full]
 ]

Answer 2

Update 3: From the function Charting`iBoxWhiskerChart we get the full list of built-in settings for Joined:

Grid[{{Automatic | All | True | 
     "Median", {{Mean[#1[[1]]], Quantile[#2, 0.5`]} &}},
   {"Mean", {{Mean[#1[[1]]], Mean[#2]} &}},
   {"Max", {{Mean[#1[[1]]], Max[#2]} &}},
   {"Min", {{Mean[#1[[1]]], Min[#2]} &}},
   {"LowerQuartile", {{Mean[#1[[1]]], Quantile[#2, 0.25`]} &}},
   {"UpperQuartile", {{Mean[#1[[1]]], Quantile[#2, 0.75`]} &}},
   {None | False, {}}}, Dividers -> All] // 
 Style[#, 20, ShowStringCharacters -> True] &

Update 2: It also turns out that, in both BoxWhiskerChart and DistributionChart, the option Joined has a few built-in settings such as "Mean","Min", "Max", "Median" (in addition to arbitrary pure functions shown in the original answer.)

SeedRandom[1]
data = RandomVariate[LogNormalDistribution[1, .5], {10, 100}];

Row[BoxWhiskerChart[data, Joined -> #, 
      PlotLabel -> Style[Row[{"Joined  -> ", "\"", #, "\""}], 16, "Panel"], 
      ChartStyle -> "Pastel", ImageSize -> 250] /. l : Line[__] :> {#2, Thick, l} & @@@ 
   Transpose[{{"Min", "Mean", "Median", "Max"}, {Red, Green, Blue, Orange}}]]

It seems that only a single line can be produced using Joined. To get multiple lines, we can Show multiple charts with different Joined settings:

colors = {Red, Green, Blue, Orange};
i = 1; 
Show[BoxWhiskerChart[data, Joined -> #, 
     ChartBaseStyle -> {EdgeForm[Opacity[.1]], FaceForm[]}, 
     ChartStyle -> "Pastel"] & /@ {"Min", "Max", "Mean", "Median"}] /. 
 l_Line :> {colors[[i++]], Thick, l}

Using DistributionChart in place of BoxWhiskerChart above we get

and

Update: A pure function setting for Joined also works for BarChart. Such functions apply to the list of horizontal and vertical ranges {{xmin, xmax}, {ymin, ymax}} of the rectangles:

BarChart[{{3, 3, 4, 1}, 2 + {3, 3, 4, 1}}, Joined -> (Mean /@ # & )] /. 
 l : Line[x_ /; (x[[1, 2]] =!= 0.)] :> {Red, Thick, l}

BarChart[{{3, 3, 4, 1}, 2 + {3, 3, 4, 1}}, Joined -> (Max /@ # & )] /. 
 l : Line[x_ /; (x[[1, 2]] =!= 0.)] :> {Red, Thick, l}

Original Answer:

BoxWhiskerChart with the option Joined

It turns out that, in BoxWhiskerChart, functions can be used as the setting for the option Joined and the setting (Mean[#2] &) gives the desired result without having to use ListLinePlot:

BoxWhiskerChart[{a, b, c}, "Mean", Joined -> (Mean[#2] &), ChartStyle -> "Pastel"]

If desired, post-process to style the line

BoxWhiskerChart[{a, b, c}, "Mean", Joined -> (Mean[#2] &), ChartStyle -> "Pastel"] /. 
  l : Line[__] :> {Red, Thick, l}

Another example:

SeedRandom[1]
data = RandomVariate[NormalDistribution[], {10, 100}];

BoxWhiskerChart[data, "Mean", Joined -> (Mean[#2] &), ChartStyle -> "Pastel"] /. 
  l : Line[__] :> {Red, Thick, l}

DistributionChart with the option Joined

Joined works the same way in DistributionChart.

DistributionChart[{a, b, c},  Joined -> (Mean[#2] &), 
  ChartElementFunction -> "PointDensity", ChartStyle -> "Pastel"] /. 
 l : Line[__] :> {Red, Thick, l}

DistributionChart[data,  Joined -> (Mean[#2] &), 
  ChartElementFunction -> "PointDensity", ChartStyle -> "Pastel"] /. 
 l : Line[__] :> {Red, Thick, l}