How to Read a Stem-and-Leaf Plot: A Simple Guide

A stem-and-leaf plot displays a set of numbers in an organized list while preserving the original values. The stems group numbers by place value; the leaves show the remaining digit or digits. For example, in a plot keyed as 4 | 7 = 47, the stem 4 and leaf 7 represent 47. Once you know the key, you can read individual data points, count them, and spot clusters, gaps, and extremes.

You do not need special tools. You do need the complete plot, including its key, and a clear idea of the units or scale being used. If the key is missing, check the assignment or source before interpreting the numbers: different plots can use different scales.

What You’ll Need

The stem-and-leaf plot, with all stems and leaves visible.
The key or legend that explains how to combine a stem and leaf.
Paper or a calculator if you want to record, count, or summarize many values.

Step-by-Step

Find the key. Look for a note such as 3 | 6 = 36. It tells you how the digits fit together and what place value they represent. In this example, the stem is the tens digit and the leaf is the ones digit. Do not assume the plot uses whole numbers or the same scale as another example.
Identify the stems and leaves. The stems are usually listed in a vertical column on the left of a divider. Leaves appear to the right of the divider, grouped in rows beside their stems. A row might look like 2 | 1 4 8. The divider is a separator, not a decimal point or an arithmetic sign.
Join each stem to each leaf. Use the key’s place-value rule to combine the stem with every leaf in its row. If 2 | 1 4 8 means 21, 24, and 28, then that row represents three observations. Each leaf makes one complete data value; do not read the entire row as one number.
Read the whole plot in order. Start at the smallest stem and move downward through the rows. Within a row, read each leaf separately. Leaves are commonly arranged from least to greatest, but check the display rather than relying on that convention. The values may represent measurements, scores, ages, or another quantity; keep the stated units in mind.
Count the data points. Count the leaves, not the stems. Every leaf represents one observation, so a row with four leaves contains four values even though it has just one stem. The total number of leaves is the number of observations represented, unless the plot explicitly says otherwise.
Find the smallest and largest values. The first leaf in the lowest occupied stem will usually give the minimum, and the last leaf in the highest occupied stem will usually give the maximum when leaves are sorted. Confirm the key and leaf order, then combine the digits to state the actual values.
Look for patterns. Rows with many leaves show where values are concentrated; sparse rows or empty stems can show gaps. The ends of the plot reveal the range of values. A stem-and-leaf plot can help you notice these features, but do not claim a cause or a trend that the data alone does not establish.
Check your interpretation. Reconstruct several values, including one at each end of the plot, and compare them with the key. If the data set is small, list all reconstructed values and check that the count and order make sense. This catches errors such as dropping a digit or assigning a leaf to the wrong row.

For example, suppose a plot has the key 4 | 2 = 42 and the row 4 | 2 5 9. The values in that row are 42, 45, and 49. It contains three observations. If the next row is 5 | 1 3, those values are 51 and 53; the full plot is read by combining each stem separately with each leaf.

Common Mistakes

Skipping the key: A stem and leaf do not have one universal scale. A key may represent whole numbers, decimal values, or values with more than one digit in the stem.
Reading a row as one number: In 4 | 2 5 9, the leaves are three separate observations, not the number 4259.
Counting stems instead of leaves: One stem can represent many observations. Count every leaf to find the data-set size.
Confusing the divider with a decimal point: The line separates stems and leaves. Only the key tells you whether the values are decimals or whole numbers.
Assuming every stem has leaves: An empty stem may be included to preserve the scale and show a gap. It is not an extra observation.
Ignoring repeated leaves: Repeated leaves usually represent repeated values, not a printing error. Keep each one when counting or reconstructing the data.
Forgetting units or negative signs: The plot may show a measurement in a particular unit, or use a convention for negative values. Read any labels or notes before reporting values.

Tips

Say the key aloud in plain language before reading: “4 | 7 means 47,” for example.
Use a place-value chart if the stem has multiple digits or the key seems unfamiliar.
Mark each leaf as you read it if the plot is dense; this helps prevent skipping or counting it twice.
When comparing two plots, confirm that both use the same key, units, and scale. Similar-looking rows may represent different values.
When you need the median or another summary, first write the values in order. Do not estimate from the shape if an exact result is required.

Troubleshooting

The key is missing: Look for a caption, instructions, or an example elsewhere on the page. If you cannot confirm what a stem and leaf mean, ask whoever provided the plot. You can describe the pattern of digits, but should not state the exact values as certain.

A leaf has more than one digit: Check the key. Some plots use a leaf that contains multiple digits, or stems that include more than one digit. Follow the stated grouping rather than splitting digits by habit.

The leaves are out of order: You can still combine each leaf with its stem to recover the values. Sort the reconstructed values if you need to find the minimum, maximum, median, or another ordered summary. Do not alter the original plot when reporting its arrangement.

The plot seems inconsistent: Recheck the divider, key, labels, and whether a stem was split into multiple rows. If the number of leaves does not match a stated sample size, a value may be missing or the plot may have been copied incorrectly. Flag the mismatch rather than silently changing the data.

Frequently Asked Questions

What does one leaf represent?

One leaf represents one data value, read together with its stem according to the key. Repeated leaves generally indicate repeated observations.

How do I find the mode?

Reconstruct the values and find which value appears most often. Repeated leaves on the same stem can show a repeated value directly.

Can a stem-and-leaf plot show decimal numbers?

Yes. The key may show that the stem and leaf represent tenths, hundredths, or another place value. Use that key rather than assuming the values are whole numbers.

What does a stem with no leaves mean?

It usually indicates that no observations fall in that part of the scale. An empty stem may be kept to show the spacing between occupied rows.

Is a stem-and-leaf plot the same as a histogram?

No. Both can show how values are distributed, but a stem-and-leaf plot preserves individual data values. A histogram groups values into intervals and displays counts for those groups.

Further reading: National Council of Teachers of Mathematics. Details can change, so check the official page for anything that matters to you. Spotted a mistake? Tell us. How we write an answer.