A stem-and-leaf diagram, also called a stem and leaf plot( stemplot), is used for presenting quantitative data in a graphical format and it quickly summarizes the data by maintaining the individual data points. Stem-and-leaf displays retain the original data to at least two significant digits.

The "stem" is a column of the unique elements of data after removing the last digit and the final digits ("leaves") of each column are then placed in a row next to the appropriate column and sorted in numerical order.The advantage of stem-and -leaf diagrams is that you will not incur information loss in the process of data presentations.

1. Each score is broken into two pieces, the stem and leaf.

2. The tens digits are stems, and the ones digits form the leaves.

3.The resulting stem plot produces a distribution of the data similar to a histogram, but all of the data values are retained in a compact form and it is a method used to organize statistical data.
For example, suppose we have a collection of algebra test scores

56, 65, 98, 82, 64, 71, 78, 77, 86, 95, 91, 59, 69, 70, 80, 92, 76, 82, 85, 91, 92, 99, 73

  1. Now arranging the scores in ascending order we have,
  2. 56, 59, 64, 65, 69, 70, 71, 73, 76, 77, 78, 80, 82, 82, 85, 86, 91, 91, 92, 92, 95, 98, 99
  3. As we see that the data ranges from 56 to 99, so we will have a stem from 5 to 9.The stem is plotted vertically and each number is assigned to the graph by pairing the units digit, or leaf, with the correct stem.

Creating Stem and Leaf Plot

So now the score 56 is plotted by placing the units digit, 6, to the right of stem.Stem and Leaf Plot represents an Histogram when turned vertically.So from the above we can see that the lowest and highest scores on the algebra test are 56 & 99 respectively.Mostly students have scored in the range of 90 to 99.

Suppose the subjects in a psychological study were timed while completing a certain task. Complete a stem-and-leaf plot for the following list of times:

23.25, 24.13, 24.76, 24.81, 24.98, 25.31, 25.57, 25.89, 26.28, 26.34, 27.09

In this case the stem-and-leaf plot will be enormously long, as the values are so spread out. (With the numbers' first three digits ranging from 232 to 270.) Here we will round off the given numbers, to the nearest tenth, and then use those new values for my plot.

So the above data would be,

23.3, 24.1, 24.8, 24.8, 25.0, 25.3, 25.6, 25.9, 26.3, 26.3, 27.1

So the plot now would look like:

    Stem and Leaf Plot with Decimals

Illustration 1:
Consider the set of values:
15,18, 21, 33, 40, 46, 48, 75, 92, 98, 99
Class Interval Frequency
10-30 3
30-50 4
50-70 0
70-90 1
90-110 3

For the above data we plot a histogram as shown below:

Stem and Leaf Plot Examples
Here shading the bars in a histogram is done to differentiate the bars.

The disadvantage of using histogram is while the frequency of each class is easy to see, the original data points have been lost.

So here is the Stem plot for the given data
.
Stem Leaf Plot Example
The original values can still be determined; from that bottom leaf, that the two values in the ninety's are 92, 98 and 99.