I have to present data in a very concise form. Presenting the graph is all I have space for, but I _must_ have the mean available to view somehow. Typically I use box plots with individual data points shown because the number of data points is small. That allows people to compare whether one data set was more tightly distributed than another, whilst simultaneously showing (for those who can be bothered to look) whether there were multiple outliers that are artificially skewing the mean.
The way I use statistics is impure. I am sure that many people would have a problem with the way that I treat outliers, and I am sure many people are wondering why I combine a box plot and an individual data plot. If the data isn't good enough to build a reasonable box plot then don't plot one, right? However, you have to speak the same language as your audience, and if they won't buy into your conclusions unless you show them a box plot then you have to show them a box plot.
thanks for your thoughts
Ben