017. Stem – And – Leaf Designs

The stem-and-leaf design is an alternative to a histogram, which provides a quick visual impression of the number of observations in a class. The stem-and-leaf design was devised by a noted statistician John Tukey.

Each observation in the data set is divided into two parts; a Stem and a Leaf. Although there is considerable flexibility in the procedure to be followed, it is often convenient to identify all but the last digit of an observation as the stem. The last digit is then identify as the leaf.

The stems must be placed in an ordered array from the lowest to highest. It is also often desirable to place the values in the leaf in an ordered array. The complete stem-and-leaf design for the data on passengers in Table 2.1 is presented in Table 2.12.

Table 2.12 – Stem-and-Leaf Design for Passenger Data

Stem	Leaf
5	0, 7, 9
6	0, 5, 6, 7, 8, 9, 9
7	0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 9, 9
8	0, 0, 1, 2, 3, 3, 3, 4, 4, 4, 5, 6
9	0, 1, 2, 3, 3, 4, 5, 7
10	1, 2

Now it is apparent that not only are there three observations in the 50s, but their individual values of 50, 57, and 59 are easily seen; the observations range from a low of 50 to a high of 102.

As it can be seen, the Stem-and-leaf design is similar to a histogram, but offers the advantage of retaining the values of the original observations.

If the data set contains fractional observations, like these 26.0, 28.3, 28.7, 27.8, 29.3, 29.5, it might be advantageous to use as the stem all the digits to the left of the decimal point, while those on the right become the leaf. See Table 2.13

Table 2.13 – Stem-and-Leaf Design for Fractional Observations

Stem	Leaf
26	0
27	8
28	3, 7
29	3, 5

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