How to interpret a Box-Percentile Plot?

Question

How to interpret a box-percentile plot and find the outliers? I have been trying to find an example online but so far not been successful. Here is an example diagram:

Answer 1

What this seems to be is

• a cumulative distribution function with the median and quartiles marked
• folded over at the median
• rotated $90^\circ$ and duplicated left and right

with the chart below attempting to reproduce these three steps for the iris setosa sepal widths (your left plot) with the median and quartiles shown in grey

This chart emphasises the median as the widest part and the mean absolute deviation from the median as the area. It does not give a sense of the density or probability mass function. Extreme values are at the top and bottom (outliers is a rather loaded term, and the nearest you get one here is the the value of $2.3$ illustrated at the bottom when the next lowest value is $2.9$)

As you seem to have spotted, the $60\%$ quantile is the point in the top half of the plot where the width is $0.8$ times the width of the median or $1.6$ times the width of the quartile, while the the $5\%$ quantile is the point in the top half of the plot where the width is $0.1$ times the width of the median or $0.2$ times the width of the quartile