Sources & Methodology
Methodology: Stem = floor(value / leaf_unit). Leaf = round(abs(value) mod leaf_unit). Values sorted ascending before plotting. Each stem listed once; leaves listed sorted within each row. Summary statistics: mean = sum/n; median = middle value for odd n, average of two middle values for even n; Q1 = median of lower half (below median position); Q3 = median of upper half (above median position); IQR = Q3 minus Q1; range = max minus min. Distribution shape determined by comparing mean vs median and leaf density patterns. Outlier detection: values beyond Q1 minus 1.5*IQR or Q3 plus 1.5*IQR are flagged.
Last reviewed: March 2026 — plot construction methodology verified against NCTM data analysis standards and AP Statistics curriculum guidelines.
Stem-and-Leaf Plot Calculator -- Complete Guide to Creating and Reading Stemplots
A stem-and-leaf plot is a data display method taught in middle school and high school statistics that preserves every individual data value while visually showing the distribution shape. Unlike a histogram that only shows frequency counts per interval, a stemplot lets you read the actual values, find the exact median, compute quartiles, and spot outliers — all from a single compact display.
How to Read a Stem-and-Leaf Plot -- Step by Step
Each row of a stem-and-leaf plot represents one stem value. The stem appears to the left of the vertical bar separator, and leaves extend to the right. To reconstruct any data value, combine the stem with one leaf. A stem of 4 with a leaf of 7 represents the value 47 (when leaf unit = 1, meaning leaves are ones digits).
Example: Test scores for 15 students
1|2 7
2|3 8 9
3|4 9
4|1 4 5
5|1 5
6|3 7
7|2
Key: 4 | 1 = 41 · Leaf unit = 1 · n = 15 values
Finding the Median and Quartiles from a Stemplot
One of the main advantages of a stem-and-leaf plot over a histogram is the ability to find exact summary statistics directly from the display. For the 15-value example above:
| Statistic | How to Find It | Value |
|---|
| Median (Q2) | Count to position (n+1)/2 = 8th leaf | 41 |
| Q1 (Lower Quartile) | Median of lower 7 values (positions 1-7) | 28 |
| Q3 (Upper Quartile) | Median of upper 7 values (positions 9-15) | 55 |
| IQR | Q3 minus Q1 = 55 minus 28 | 27 |
| Range | Max minus Min = 72 minus 12 | 60 |
Stem-and-Leaf Plot vs Histogram -- When to Use Each
The key decision factor is data set size. For 15 to 50 data values, a stem-and-leaf plot is preferred because it preserves individual values and allows direct computation of medians and quartiles. For data sets over 50 to 100 values, the stemplot becomes too crowded to read clearly and a histogram or box-and-whisker plot is more appropriate. For very small data sets under 15 values, a dot plot or simple list is often clearer than a stemplot.
In AP Statistics and college introductory statistics courses, stem-and-leaf plots are most commonly used for exploratory data analysis (EDA) on small data sets, comparing two distributions using back-to-back stemplots, and as a first-pass visualization before deciding which inferential tests to apply based on the observed distribution shape.
💡 Leaf unit selection tip: The leaf unit determines how to split your numbers. For two-digit data like test scores 12-99, use leaf unit = 1 (stems are tens, leaves are ones). For three-digit data like 100-999, use leaf unit = 10 (stems are hundreds, leaves are tens). For decimal data like 3.2 or 4.7, use leaf unit = 0.1 (stems are whole numbers, leaves are tenths). If your stemplot has too few rows (under 5 stems), consider splitting stems to show more detail.
Frequently Asked Questions
What is a stem-and-leaf plot? +
A stem-and-leaf plot (stemplot) organizes quantitative data by splitting each value into a stem (typically the tens digit or leading digits) and a leaf (the trailing digit). Stems are listed vertically and leaves extend horizontally right of a vertical bar separator. The plot shows distribution shape while preserving every individual data value -- more informative than a histogram for data sets of 15 to 50 values.
How do you make a stem-and-leaf plot? +
To create a stem-and-leaf plot: (1) Sort all data values. (2) Identify the stems -- all digits except the final digit. (3) List unique stems vertically in order. (4) Write each corresponding leaf to the right of its stem separated by a vertical bar. (5) Sort leaves within each row. (6) Add a key like "4 | 7 = 47" showing how to read a stem-leaf pair as a complete value.
What is the key in a stem-and-leaf plot? +
The key explains how to read one stem-leaf combination as a complete data value. For example, the key "3 | 5 = 35" means stem 3 with leaf 5 represents the number 35. The leaf unit in the key indicates the place value: leaf unit 1 means leaves are ones digits (standard), leaf unit 0.1 means leaves are tenths for decimal data, and leaf unit 10 means leaves are tens digits for three-digit data.
How do you find the median from a stem-and-leaf plot? +
Count the total number of data values (n). For odd n, the median is at position (n+1)/2 counting leaves left-to-right, top-to-bottom. For even n, average the values at positions n/2 and (n/2)+1. For 15 values, count to the 8th leaf -- that is the median. For 16 values, average the 8th and 9th leaves.
What is the difference between a stem-and-leaf plot and a histogram? +
A stem-and-leaf plot preserves every individual data value while showing distribution shape, making it more informative for data sets of 15 to 50 values. A histogram groups data into bins showing only frequency counts -- losing individual values. For data sets over 50 to 100 values, histograms are more practical as stemplots become too crowded. Stem-and-leaf plots allow exact computation of median, quartiles, and outlier detection directly from the display.
What does the shape of a stem-and-leaf plot tell you? +
The shape reveals the data distribution. A symmetric shape with roughly equal leaves on both sides of the median indicates approximately normal distribution. A right-skewed shape has values clustered at lower stems with a long right tail. A left-skewed shape has a long left tail. Isolated stems with far fewer leaves than neighbors may indicate outliers or natural data gaps. Comparing the mean and median confirms the skew direction.
When should you use a stem-and-leaf plot? +
Use a stem-and-leaf plot for data sets with 15 to 50 values when you need to see individual values, find exact medians and quartiles, or teach distribution concepts in a statistics class. Ideal for test score analysis, sports statistics, scientific measurements, and classroom data analysis tasks. For smaller data use dot plots; for larger data use histograms or box plots.
What is a back-to-back stem-and-leaf plot? +
A back-to-back stemplot compares two data sets sharing the same central stems. One data set has leaves extending left and the other extends right. This allows direct visual comparison of two distributions -- comparing test scores between two classes, measurement data between two groups, or any two data sets with overlapping range. The shape, center, and spread of each distribution can be compared at a glance.