Stem-and-Leaf Plots

A stem-and-leaf plot is a way to organize a list of numbers so you can see both the individual data values and the overall shape of the data at the same time. Each number is split into two parts: a stem, which is the leading digit (or digits), and a leaf, which is the last digit. The stems are listed once in a column, and every leaf that belongs to a stem is written next to it, usually in increasing order.

For example, the number 27 has a stem of 2 and a leaf of 7. The number 34 has a stem of 3 and a leaf of 4. Grouping numbers this way keeps every original value visible, unlike a histogram or bar graph, which only shows totals inside grouped intervals. If you want to compare how a stem-and-leaf plot stacks up against those other displays, see frequency distribution and histograms and advantages and disadvantages of bar graphs.

Look at the plot below for the data set 12, 15, 18, 21, 23, 23, 27, 34, 36, 41. The stems are 1, 2, 3, and 4, and each row lists every leaf that pairs with that stem.

The small note at the bottom, called the key, tells you exactly how to reconstruct a value. Here, "1 | 2 means 12" tells you the stem is the tens digit and the leaf is the ones digit. Always check the key before reading any stem-and-leaf plot, because the place value the stem represents can change depending on the size of the data (for example, a stem could represent hundreds instead of tens).

Once a plot is built, you can quickly find the minimum (12), the maximum (41), and how many values fall in each stem group, which gives you a fast sense of the shape of the distribution, such as whether the data clusters toward one end or spreads out evenly.

Follow these steps to build a stem-and-leaf plot from a raw list of numbers:

1. Order the data. Arrange all values from least to greatest. This makes it much easier to sort the leaves later.
2. Choose the stems. Decide which digit or digits will act as the stem based on the place value of your data. For two-digit numbers, the stem is usually the tens digit.
3. List each stem once. Write every stem that appears in the data down a column, from smallest to largest, with no repeats.
4. Attach the leaves. Go through the ordered data and write each number's leaf digit next to its matching stem, in increasing order.
5. Add a key. Include a short note such as "3 | 4 means 34" so anyone reading the plot knows how to interpret it.

Worked Example

Suppose a class recorded the following quiz scores out of 50: 22, 35, 41, 38, 22, 47, 19, 35, 41, 28.

Step 1: Order the data: 19, 22, 22, 28, 35, 35, 38, 41, 41, 47.

Step 2: The stems are the tens digits: 1, 2, 3, 4.

Step 3 and 4: List each stem with its leaves.

• 1 | 9
• 2 | 2 2 8
• 3 | 5 5 8
• 4 | 1 1 7

Step 5: Key: 1 | 9 means 19. From this plot you can instantly see that most scores landed in the 30s and 40s, and that 22 and 41 were each repeated exactly once each pair.

A back-to-back stem and leaf plot compares two related data sets by sharing one column of stems in the middle, with one group's leaves branching to the left and the other group's leaves branching to the right. This is especially useful for comparing, for example, test scores between two classes.

To read a back-to-back plot, leaves on the left side are usually listed with the smallest leaf closest to the stem, so the row still reads outward from the middle in increasing order. Comparing the two sides row by row lets you see quickly whether one group's values tend to run higher, lower, or more spread out than the other.

• Do not skip a stem just because it has no leaves. If your data ranges from 12 to 41, the stem 0 is not needed, but every stem from 1 through 4 should appear, even if a row is left blank.
• Keep leaves in increasing order within each row so the plot is easy to scan.
• Watch the key carefully. A stem-and-leaf plot for data in the hundreds might use a key like "12 | 3 means 123," where the stem itself has two digits.
• A double stem-and-leaf plot (splitting each stem into two rows, such as 0 to 4 and 5 to 9) can be used when a single stem would collect too many leaves to read comfortably.

A stem-and-leaf plot works best for small to medium data sets where you want to preserve every individual value while still seeing the overall spread. For larger data sets or when you only care about totals within ranges, a histogram may communicate the pattern more clearly; for categorical data, a bar graph is usually the better tool. Reviewing the shapes of distributions can help you decide which display best highlights the pattern in your data.

Related lessons

• Statistics Help