Visualization/colorization of many outliers in a BoxWhiskerChart

Question

Imagine a larger data set which I want to display using BoxWhiskerChart.

data = Flatten[{RandomReal[1., 10000], RandomReal[2., 2000]}];

BoxWhiskerChart[data, {"Median", {"MedianMarker", 1, Black}, {"Whiskers", Black},
{"Fences", 0.5, Black}, {"Outliers", "o", Black}}]

Since there are a lot of outliers I cannot visualize them properly - the potential reader only sees a thick black line. When I enlarge the outlier marker the whole thing does not get better at all.

BoxWhiskerChart[data, {"Median", {"MedianMarker", 1, Black}, {"Whiskers", Black},
{"Fences", 0.5, Black}, {"Outliers", Style["o", 100], Black}}]

Is there a way to colorize the outlier markers using something like ColorFunction (which did not work for me) in a way that the individual markers can be seen more distinctly (alternating black, gray etc.)?

Or would it even be possible to reduce the number of displayed outliers in a way that one can see/identify them better?

UPDATE

I have decided to display the data using DistributionChart which clearly has advantages of showing the actual value distribution of the data. But with this solution another problem arises (see here).

Answer 1

Until someone comes up with a less convoluted approach, you can post-process the output of BoxWhiskerChart to color and/or to downsample the outliers as follows:

data = Flatten[{RandomReal[1., 10000], RandomReal[2., 2000]}];

b1 = BoxWhiskerChart[data, 
     {"Median", {"MedianMarker", 1, Black}, {"Whiskers", Black}, {"Fences", 0.5, Black}, 
     {"Outliers", Graphics[{RGBColor[0, 1, 0], Line[{{0, 0}, {1, 0}}]}]}},
     ImageSize -> 400];

b2 = b1 /. InsetBox[GraphicsBox[{RGBColor[0, 1, 0], ___}, ___], ___] :> {}

epl = Cases[b1, ib : InsetBox[GraphicsBox[{ RGBColor[0, 1, 0], ___}, ___], ___] :>
                          (ib /. RGBColor[0, 1, 0] -> Hue[RandomReal[]]), {0, Infinity}];

bwcs = Partition[Prepend[Show[b2, Epilog->epl[[#]]]&@@@{{ ;; }, {;; ;; 10}, {;; ;; 50}}, b1], 2];
Grid[bwcs]