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Using data as graphic elements: stem and leaf displays

Charts and tables are often regarded as alternative views. As discussed a while back, graphic tables unite the advantages of both visualization forms without any of the usual disadvantages. Graphic elements lend helpful orientation to the human eye. Numbers deliver the details. There are no problems with legends or value placements.

Semi-graphic visualizations, a brilliant example from John W. Tukey, transform the actual data into graphic elements. As with many great ideas, this one has been around for a long time but hasn’t been widely used. The most famous example is the stem and leaf display.

The first example illustrates this principle based on age distribution. Here is how to read it: The numbers to the left (the “tree”) express the tens column while those to the right (the “leaves”) represent the ones column. The tens are halved and the 100 people are grouped into intervals of 5 years. You should see a person who is 21 years old, one who is 22, two who are 24, one who is 25, and so on.

2 . 1244
2 . 56777788889
3 . 111122233344
3 . 55555666667777777889999
4 . 0011111222334
4 . 55567777888999
5 . 22233344
5 . 555678
6 . 0014
6 . 55555

The second example demonstrates that you can also visualize value distributions of two groups in a three-dimensional manner. Mind you, the value to the right is pieced together as normal. One test person delivered the value 213. Three delivered the value 203. The values to the left, however, are read differently. The values 279 and 189 were only given once. It is nice to see how the left distribution is affected by their outliers.

9 27
21 3
20 3, 3, 3, 5
19 4, 5, 8
9 18 0, 2
5, 2 17 2
9, 8, 0 16
1 15

What I find most fascinating is that you can create a chart with graphic qualities with a simple text editor! Just be sure to use a monospace font, like Courier.