Stem-leaf diagram

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The stem-leaf diagram (also branch-leaf or stem-leaf diagram and, in English, stem-and-leaf plot or stemplot ) is a graphic tool for descriptive and exploratory statistics . John W. Tukey is considered the developer of this type of diagram .

Similar to the histogram or the box plot , the stem-leaf diagram is used to visualize frequency distributions . In contrast to the former, the representation of the values ​​of each individual observation is retained with the desired accuracy . Statistical indicators such as modal value , median and quantile can be read from a stem-leaf diagram . However, this type of display has its limits when it comes to a large number of features.

construction

The diagram consists of two columns. The left column contains, as "logs", the equivalence classes into which the depicted on the right side as "leaves" features are classified. Classification according to the decimal system is typical , but other subdivisions are also possible, for example using the first two digits as the stem. The rule of thumb for the number of equivalence classes is where n is the number of data records.

example

A series of measurements resulted in the following, already ordered, data:

         0,3    0,4    2,5    2,5    2,6    2,7    2,8    3,5    3,7

If you choose the natural numbers as a class division, you get the following stem-leaf diagram. So that the diagram can be read correctly, it is important to specify the unit used to create it:

3 | 5 7
2 | 5 5 6 7 8
1 |
0 | 3 4
Einheit = 0,1

With a modified stem-leaf diagram, two distributions can be compared visually. Assume that there is a second series of measurements with the following data:

0.4 1.2 1.8 2.1 2.1 2.9

Now you can write this on the left side of the "trunk":

      | 3 | 5 7
1 1 9 | 2 | 5 5 6 7 8
  2 8 | 1 |
    4 | 0 | 3 4
Einheit = 0,1

Individual evidence

  1. ^ Jürgen Janssen, Wilfried Laatz: Statistical data analysis with SPSS for Windows . 6th edition. Springer, 2007, p. 241 .
  2. Bernd Rönz, Hans G. Strohe (1994), Lexicon Statistics , Gabler Verlag, p. 344

literature

  • Dankwart Vogel, Gertrud Wintermantel: Exploratory data analysis - actively learning statistics, handouts for the teacher . Ernst Klett Verlag, ISBN 3-12-720049-8

Web links