Stem and Leaf Plot

Using the data set’s numbers themselves to form a diagram, the stem and leaf plot (or simply, stemplot) is a histogram-style tabulation of data developed by John Tukey.

Consider the following data set, sorted in ascending order: 8, 13, 16, 25, 26, 29, 30, 32, 37, 38, 40, 41, 44, 47, 49, 51, 54, 55, 58, 61, 63, 67, 75, 78, 82, 86, 95

A stem and leaf plot of this data can be constructed by writing the first digits in the first column, then writing the second digits of all the numbers in that range to the right.

Stem and Leaf Plot

0|8

1|3 6

2|5 6 9

3|0 2 7 8

4|0 1 4 7 9

5|1 4 5 8

6|1 3 7

7|5 8

8|2 6

9|5

The result is a histogram turned on its side, constructed from the digits of the data. The term “stem and leaf” is used to describe the diagram since it resembles the right half of a leaf, with the stem at the left and the outline of the edge of the leaf on the right. Alternatively, some people consider the rows to be stems and their digits to be leaves.

If a larger number of bins is desired, the stem may be 2 digits for larger numbers, or there may be two stems for each first digit – one for 2nd digits of 0 to 4 and the other for 2nd digits of 5 to 9.

Stem and Leaf Plot Advantages

The stem and leaf plot essentially provides the same information as a histogram, with the following added benefits:

- The plot can be constructed quickly using pencil and paper.
- The values of each individual data point can be recovered from the plot.
- The data is arranged compactly since the stem is not repeated in multiple data points.
- The stem and leaf plot offers information similar to that conveyed by a histogram, and easily can be constructed without a computer.