The Stem-and-Leaf Plot

The stem-and-leaf plot is a way of showing a distribution of data in a visual, histogram-like manner, and is an excellent way to explore the data's shape, location, and spread. It is an excellent way to begin an analysis of a single variable.

Stem-and-leaf plots are covered in HS167.

To illustrate stem-and-leaf plots, let us consider a data set with the following numerical values: 21, 42, 5, 11, 30, 50, 28, 27, 24, and 52.

To start, a stem-like axis that extends from the data set's minimum to its maximum is created:

|5|

|4|

|3|

|2|

|1|

|0|

(x 10)

An axis multiplier accompanies the stem in order to allow the viewer to decipher the magnitude of each data point.

Data are then rounded to show only two (or three) significant digits. The second (or third) significant digit of each data point is then plotted against the stem-like axis. For example, a value 21 is shown as:

|5|

|4|

|3|

|2|1

|1|

|0|

(x 10)

The remaining data points are plotted:

|5|02

|4|2

|3|0

|2|1874

|1|1

|0|5

(x 10)

Notice data are now sorted in approximate rank order, and the shape, location and "spread" of the distribution is clearly visible. Also notice that the stem-and-leaf plot leaves the data intact for future calculations.

The next illustrative example shows how the stem-and-leaf plot can be modified to accommodate data that might not immediately lend themselves to this type of plot. Suppose, for example, this new data set:

1.47, 2.06, 2.36, 3.43, 3.74, 3.78, 3.94

Notice how data include more than 2 significant digits and have decimal point values. In such situations, we round the data to two significant digits. For example, the above values are rounded to 1.5, 2.1, 2.4, 3.4, 3.7, 3.8, and 3.9. The decimal points are ignored, and using stem values of 1, 2, and 3, we get the following stem-and-leaf plot:

|1|5

|2|14

|3|4789

(x 1)

Realizing that this plot is somewhat squashed, we could spread it out by splitting the stem using double values, with the first value reserved for values leaf values between 0 and 4, and the second stem-value reserved for leaf values of 5 through 9. For example, we could plot:

|1|

|1|5

|2|14

|2|

|3|4

|3|789

(x 1)

There are an infinite number of possibilities one can ponder when drawing stem-and-leaf plots. In general, the best graph is the one that addresses the question one hopes to answer while providing the most information about the data's shape, location, and spread.