Stem-and-Leaf Plot — Definition, Formula & Examples
A stem-and-leaf plot is a way to display numerical data where each value is split into a "stem" (the leading digit or digits) and a "leaf" (the last digit), so you can see both the shape of the distribution and every individual data point.
A stem-and-leaf plot (also called a stemplot) is a statistical data display that partitions each observation into a stem, consisting of all digits except the rightmost, and a leaf, consisting of the final digit. Leaves sharing the same stem are listed in a single row, typically sorted in ascending order. The result is a semi-graphical representation that preserves the original data values while simultaneously revealing the distribution's shape, center, and spread.
How It Works
To build a stem-and-leaf plot, first decide which digits form the stem and which digit becomes the leaf. For two-digit numbers, the tens digit is the stem and the ones digit is the leaf. Write the stems in a vertical column from smallest to largest, then draw a vertical line to the right. For each data value, place its leaf next to the matching stem. Once every value has been recorded, reorder the leaves in each row from smallest to largest. Reading across any row tells you all data values that share that stem, and looking at the lengths of the rows gives you a quick picture of where data clusters.
Worked Example
Problem: Create a stem-and-leaf plot for these 12 test scores: 82, 75, 91, 68, 85, 77, 93, 72, 88, 81, 76, 90.
Step 1: Identify the stems. The tens digits range from 6 to 9, so the stems are 6, 7, 8, and 9.
Step 2: Split each value. For example, 82 has stem 8 and leaf 2; 75 has stem 7 and leaf 5. Do this for every score.
Step 3: Place the leaves next to their stems. Stem 6: 8. Stem 7: 5, 7, 2, 6. Stem 8: 2, 5, 8, 1. Stem 9: 1, 3, 0.
Step 4: Sort the leaves in ascending order within each row. Stem 6: 8. Stem 7: 2, 5, 6, 7. Stem 8: 1, 2, 5, 8. Stem 9: 0, 1, 3.
Step 5: Read the plot. The longest rows are stems 7 and 8 (four leaves each), showing that most scores fall in the 70s and 80s. The minimum is 68 and the maximum is 93.
Answer: The completed stem-and-leaf plot is:
6 | 8
7 | 2 5 6 7
8 | 1 2 5 8
9 | 0 1 3
Key: 7 | 5 means 75.
Another Example
This example uses three-digit numbers to show how the stem expands to two digits while the leaf remains a single digit.
Problem: Create a stem-and-leaf plot for these race times (in seconds): 104, 112, 118, 107, 121, 115, 109, 110, 123, 116.
Step 1: These are three-digit numbers. Use the first two digits as the stem and the last digit as the leaf. The stems needed are 10, 11, and 12.
Step 2: Place each leaf. For 104: stem 10, leaf 4. For 112: stem 11, leaf 2. Continue for all values.
Step 3: Sort leaves in each row. Stem 10: 4, 7, 9. Stem 11: 0, 2, 5, 6, 8. Stem 12: 1, 3.
Step 4: Write the final plot with a key.
10 | 4 7 9
11 | 0 2 5 6 8
12 | 1 3
Key: 11 | 2 means 112 seconds.
Answer: 10 | 4 7 9
11 | 0 2 5 6 8
12 | 1 3
Key: 11 | 2 means 112 seconds. Most times fall in the 110–118 range.
Visualization
Why It Matters
Stem-and-leaf plots appear in nearly every middle-school and introductory high-school statistics unit, and they are tested on standardized assessments like state math exams and the AP Statistics exam. Scientists and quality-control engineers use them for quick exploratory data analysis when a data set is small enough that individual values matter. Building stem-and-leaf plots also reinforces place value and sorting skills that carry into more advanced data displays like histograms and dot plots.
Common Mistakes
Mistake: Forgetting to include a key (legend).
Correction: Always write a key such as "5 | 3 means 53" so readers know how to interpret the stems and leaves.
Mistake: Using more than one digit as a leaf.
Correction: Each leaf must be exactly one digit. For the number 145, the stem is 14 and the leaf is 5 — not stem 1 and leaf 45.
Mistake: Not sorting the leaves in each row.
Correction: After placing all leaves, reorder them from smallest to largest within each stem. An unsorted plot makes it hard to find the median or spot patterns.
Check Your Understanding
Given the stem-and-leaf row "3 | 0 4 4 7 9", list all five data values.
Hint: Attach the stem (3) to each leaf to form the full number.
Answer: 30, 34, 34, 37, 39
A data set has these values: 45, 52, 58, 41, 53, 60, 47, 55. What are the stems?
Hint: Look at the tens digits of the smallest and largest values.
Answer: The stems are 4, 5, and 6.
From the plot "5 | 1 3 6 8" and "6 | 2 5", what is the median of the six values?
Hint: List all values in order, then find the middle pair.
Answer: The six values are 51, 53, 56, 58, 62, 65. The median is the average of the 3rd and 4th values: (56 + 58) / 2 = 57.