Stem-and-leaf display

This plot has been implemented in Octave and R.

A stem-and-leaf plot is also called a stemplot, but the latter term often refers to another chart type. A simple stem plot may refer to plotting a matrix of y values onto a common x axis, and identifying the common x value with a vertical line, and the individual y values with symbols on the line.

Unlike histograms, stem-and-leaf displays retain the original data to at least two significant digits, and put the data in order, thereby easing the move to order-based inference and non-parametric statistics.

Construction

To construct a stem-and-leaf display, the observations must first be sorted in ascending order: this can be done most easily if working by hand by constructing a draft of the stem-and-leaf display with the leaves unsorted, then sorting the leaves to produce the final stem-and-leaf display. Here is the sorted set of data values that will be used in the following example:

44, 46, 47, 49, 63, 64, 66, 68, 68, 72, 72, 75, 76, 81, 84, 88, 106

Next, it must be determined what the stems will represent and what the leaves will represent. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. In the case of very large numbers, the data values may be rounded to a particular place value (such as the hundreds place) that will be used for the leaves. The remaining digits to the left of the rounded place value are used as the stem.

In this example, the leaf represents the ones place and the stem will represent the rest of the number (tens place and higher).

The stem-and-leaf display is drawn with two columns separated by a vertical line. The stems are listed to the left of the vertical line. It is important that each stem is listed only once and that no numbers are skipped, even if it means that some stems have no leaves. The leaves are listed in increasing order in a row to the right of each stem.

When there is a repeated number in the data (such as two 72s), the plot must reflect such (so the plot would look like 7 | 2 2 5 6 7 when it has the numbers 72 72 75 76 77).

${\displaystyle \begin{array}{rl}\text{Stem}& \text{Leaf}\\ 4& 4679\\ 5& \\ 6& 34688\\ 7& 2256\\ 8& 148\\ 9& \\ 10& 6\end{array}}$

Key: ${\displaystyle 6\mid 3=63}$

Leaf unit: 1.0

Stem unit: 10.0

A stem-and-leaf plot can be transposed to display the leaves in vertical columns, for example:

${\displaystyle \begin{array}{cccccccc}& & & 8& & & & \\ & 9& & 8& 6& & & \\ & 7& & 6& 5& 8& & \\ & 6& & 4& 2& 4& & \\ \text{Leaf}& 4& & 3& 2& 1& & 6\\ \text{Stem}& 4& 5& 6& 7& 8& 9& 10\end{array}}$

Rounding may be needed to create a stem-and-leaf display. Based on the following set of data, the stem plot below would be created:

−23.678758, −12.45, −3.4, 4.43, 5.5, 5.678, 16.87, 24.7, 56.8

For negative numbers, a negative is placed in front of the stem unit, which is still the value X / 10. Non-integers are rounded. This allows the stem and leaf plot to retain its shape, even for more complicated data sets. As in this example below:

${\displaystyle \begin{array}{rl}\text{Stem}& \text{Leaf}\\ -2& 4\\ -1& 2\\ -0& 3\\ 0& 466\\ 1& 7\\ 2& 5\\ 3& \\ 4& \\ 5& 7\end{array}}$

Key: ${\displaystyle -2\mid 4=-24}$