Discrete Scatter Plot Visualization

Question

This is a very special plotting request, but I have data I want to view in a very particular way. Here's the situation:

1) The data I have is binned into 25 bins, each bin contains a different number of data points. The larger the bin value, the smaller then number of data points it has within it, roughly speaking (This is just a result of the data processing which was done).

[9568, 10079, 10137, 10090, 10154, 10091, 10046, 10116, 9959, 9401, 7703, 5216, 3089, 1632, 854, 466, 221, 106, 63, 27, 12, 5, 1, 0]

2) I have access to the bin values.

[ 0.02648645  0.09996368  0.1734409   0.24691813  0.32039536  0.39387258
  0.46734981  0.54082703  0.61430426  0.68778148  0.76125871  0.83473593
  0.90821316  0.98169038  1.05516761  1.12864483  1.20212206  1.27559928
  1.34907651  1.42255373  1.49603096  1.56950818  1.64298541  1.71646264]

I can easily produce an 'errorbar' type plot in matplotlib (the y-axis is scaled from radius to degrees below):

But, this is not particularly insightful for what I'd like to study. I'd really like to know if there are 'islands' of angle values within each bin, and to do this, I would need something like a scatterplot or an imshow/hexbin type plot, where the density of points can be represented by color (in the case of imshow/hexbin at least). The following is an example of what happens when represented by a regular scatterplot with the smallest marker size:

Would anybody know of a good way to generate this type of visualization?

EDIT: This may help clarify a couple of things. The following plot is a sample of what a histogram would look like for the first couple of bins. Data contained within bins seem to follow some sort of distribution (I mentioned 'islands' before, because I am not ruling out the possibility of multiple peaks in the distribution). I would like this distribution to be visualized for all bins simultaneously. In other words, is there a way to do a vertical temperature map for each bin and have them all shown on the same plot?

Answer 1

The violin plot mentioned in the comments was a nice solution to my problem. Here's where I found a python implementation of it - it would certainly be nice if this were included into matplotlib eventually. Overplotted is a box plot centered on the median value, and includes the 2nd and 3rd quartiles.