Stem and Leaf Plot Calculator

Did You Know?

How Stem-and-Leaf Works

Expert Tips

Shape Analysis

Frequently Asked Questions

Summary Statistics

Worked Example

For data: 52, 58, 62, 65, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 85, 86, 88, 90 (test scores)

5 | 2 8
6 | 2 5 8
7 | 0 2 4 5 6 8
8 | 0 2 4 5 6 8
9 | 0

Stem-and-Leaf vs Other Displays

Constructing by Hand

1. List all values and identify the range (min to max).
2. Choose stem: typically tens digit. For 52–98, stems are 5, 6, 7, 8, 9.
3. For each value, write the leaf (ones digit) next to its stem.
4. Sort leaves within each stem (ascending).
5. For back-to-back: put Group A leaves on the left (reversed), Group B on the right.
6. Add a key: e.g., "7|4 means 74" or "10|3 means 10.3" for decimals.

Decimal Data Examples

Interpreting the Plot

• Concentration: Many leaves on one stem → data clustered in that range.
• Spread: Leaves spread across many stems → wide distribution.
• Gaps: Empty stems between non-empty ones → possible outliers or natural gaps.
• Skewness: Long tail of leaves on one side → skewed distribution.
• Bimodality: Two distinct clusters of stems with many leaves → bimodal.
• Outliers: Isolated stems with few leaves far from the main cluster.

R and Python Equivalents

Best Practices

• Always include a key so readers know how to interpret stem|leaf.
• Sort leaves within each stem for easier reading and pattern recognition.
• For back-to-back, use consistent stem ranges; pad with empty cells if needed.
• Choose stem width to get 5–20 stems; too few or too many reduces usefulness.
• For presentation, consider truncating very long leaf rows or using split stems.
• Report n (sample size) alongside the plot.

Common Mistakes to Avoid

When to Use Stem-and-Leaf

Stem-and-leaf is ideal when:

• You have a small to moderate dataset (roughly 15–150 values).
• You need to preserve exact values (no binning).
• You want a quick, hand-drawn display without software.
• You are comparing two groups (back-to-back).
• Data are integers or easily converted (×10, ×100 for decimals).

For very large datasets (500+), consider a histogram instead.

Split Stems Explained

With split stems, each stem appears twice:

• 5* (or first row): leaves 0, 1, 2, 3, 4
• 5. (or second row): leaves 5, 6, 7, 8, 9

This doubles the number of stems and gives finer resolution when data are clustered (e.g., many values in the 50s).

Frequency Bar Chart

The frequency-by-stem bar chart shows how many values fall in each stem. It complements the stem-and-leaf by giving a quick visual of the distribution shape.

Tall bars indicate stems with many leaves. Use it to spot peaks (modes), gaps (empty stems), and overall spread at a glance. The bar chart is useful when presenting to audiences who may find the stem-and-leaf less familiar.

Keyboard & Usage Tips

• Paste data from Excel or CSV — comma or space separated values work.
• Use the comparison preset for back-to-back; enter two datasets.
• Toggle split stems when data are clustered in a narrow range.
• For decimals, select ×10 or ×100 and update the key description.

History & Pedagogy

John Tukey introduced stem-and-leaf displays in his 1977 book Exploratory Data Analysis. The technique was designed for hand computation and quick insight — no computer required.

Today it remains a staple in introductory statistics courses because it preserves data, reveals shape, and teaches place value. Many textbooks use it before introducing histograms. The back-to-back variant is especially useful for comparing two groups (e.g., treatment vs control, before vs after) in a compact format.

Summary Statistics Formulas

These are computed from your data and displayed in the summary statistics panel.

Official Sources