This is the first time I've seen a ternary plot, thank you for the introduction. I can see how it has limited usefulness, though. Aside from the challenge of identifying or labeling individual data points, I find it difficult to keep track of the "high/low" ends of each axis.

I think it is important to note that the ternary diagram is showing the relative amount of a component with respect to the others. In other words, the total is not important. Therefore, you can see your observations summing up to a certain constant (1 as you plotted, or 100 or whatever).
In your example, a person with a high level of Math.Stats, Technology.Programming and Business, and other person with poor level of them are going to be plotted in the same place (in the center).

It's quite useful in some geosciences, like soil science.
Classifying a soil by grain size distribution (which has all sorts of implications on how the plants can take up water, how water is retained in the soil and thus e.g. how irrigation needs to be done) is often done on a ternery diagram called texture triangle like this one:

https://i.stack.imgur.com/r7fYI.png

clay are the very small particles (not visible to naked eye), sand is what you'd typically know as grains from the beach, silt is inbetween. There's an exact definition for grain size classes, btw.

So if you have several soil samples, on the diagramm it's very easy to get a rough idea of soil texture and thus, usability for agriculture.

In case it's interesting: clay soil doesn't let water in easily (but retains nutrients well), sand doesn't hold water, silt is more prone to erosion.
So the 'optimum' soil has a mixture of all (called loam) and resides in the middle of the texture triangle.
(Yes, this is a strong symplification. Read a soil science book for the nuances and details^^)

I have to disgree with the choice of a ternary plot for this data.

Such plots are perfect when the sums of the components are constant. This is the case in the soil example that Berry posted and also for the phase diagrams for ternary alloy systems where I first encountered them.

However, looking at the data provided in the table in the original article, the sum is not constant and, therefore, this plot represents and unnecessary distortion of the data.

My personal preference would have been to take a top-down projection of the scatter plot and encode the z-axis using marker size allowing you to still group the data by color as in the original.

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