From #19860 (comment)

I'm -0.1 on this because the ascii-art is only a rough visual approximation of the box and harder to read than an actual image. It's a trade-off between having the info in the ascii docstring and readability in the html output. But I won't block a PR.

Note that if you do the ascii-art, you'll likely have to use some left-side character for aligning the ascii lines. ReST messes up if any line in the code block is less indented than the first line. See e.g. https://matplotlib.org/devdocs/api/_as_gen/matplotlib.axes.Axes.barbs.html

fwiw I think this renders just fine on the website

but let's see what others think...
(perhaps I can use "o" instead of "." for outliers, though)

Personally I would remove most of this verbiage, and just point to wikipedia and an example (assuming we have one). I agree this didn't belong in the FAQ, but I don't think it really belongs in the docstring either...

I'm fine with that as well.

I got rid of most of the verbiage, but kept the asciiart diagram and moved it to the top. I don't think it takes too much space there?
I also harmonized "box plot" to "boxplot" in the docstring.