[Evidlo]

> So you can no longer reverse the process

I've never understood this to be the purpose of a boxplot, only a means of visualizing a distribution's quartiles.

You've gotten a flood of comments from upset people, so I'll keep it short by saying that a boxplot doesn't actually do what you claim for Gaussians, as the 0 and 100 percentile "whiskers" would be at plus/minus infinity. As for a bounded bell-shaped distribution, there are several non-unique ways to define such a distribution.

[crazygringo]

> as the 0 and 100 percentile "whiskers" would be at plus/minus infinity

The point is not to plot an ideal Gaussian, the point is to plot the data.

In real life the whiskers are the actual minimum and maximum values observed.

[blueflow]

> In real life the whiskers are the actual minimum and maximum values observed.

Look at this: https://upload.wikimedia.org/wikipedia/commons/1/1a/Boxplot_...

0.7% of all values are outside the whiskers.

[crazygringo]

There are two standard ways of doing box plots. One is miniums and maximums, the other is the 1.5 IQR method.

The very Wikipedia article your image comes from explains this:

https://en.wikipedia.org/wiki/Box_plot#Whiskers