Stem and Leaf Plot
Print PageA Stem and Leaf Plot Calculator (also known as a Stem-and-Leaf Display Generator, Split-Stem Plot Maker, Back-to-Back Stem Plot Utility, or Exploratory Data Analysis [EDA] Visualizer) splits raw numerical data points into a leading Stem (the most significant digits) and a trailing Leaf (the final rightmost digit), constructing an ordered visual distribution that preserves exact original data values while displaying shape, center, and spread.
Invented for rapid exploratory data analysis, stem-and-leaf plots combine the visual histogram shape of a bar graph with the precision of a raw data table, making it effortless to identify modal classes, outliers, medians, and quartiles.
Our free online Stem and Leaf Plot Calculator provides instant calculations across all quantitative dataset parameters:
- Stem-and-Leaf Value Decomposition:
xi = ( Stemi · Multiplier ) + ( Leafi · Leaf Unit ). - Leaf Unit Legend Key: Defines the place value of the leaf digit (e.g.
Key: 7 | 2 = 72for Leaf Unit = 1.0, orKey: 7 | 2 = 7.2for Leaf Unit = 0.1). - Five-Number Summary Generation: Calculates Minimum, First Quartile (
Q1), Median (Q2), Third Quartile (Q3), and Maximum. - Interquartile Range (IQR):
IQR = Q3 - Q1. - Split-Stem Display (Optional): Splits large stems into two rows (Leaves 0–4 on lower stem, Leaves 5–9 on upper stem).
- Back-to-Back Stem Plot (Dual Comparison): Compares two distinct datasets sharing a single central stem column.
Master Stem and Leaf Plot Reference Table (High School Math Test Scores: n = 25 Students)
The table below displays the ordered stem-and-leaf construction, stem frequencies, and 5-number summary metrics for 25 student math exam scores (Key: 7 | 2 = 72 Points, Leaf Unit = 1.0):
| Stem (Tens Digit) | Ordered Leaves (Ones Digits) | Stem Row Frequency | Represented Data Values | Statistical Class Significance |
|---|---|---|---|---|
| 5 | 2, 5, 8 | 3 students | 52, 55, 58 | Minimum Value Row (Min = 52) |
| 6 | 1, 4, 4, 7 | 4 students | 61, 64, 64, 67 | Contains Q1 Boundary (Q1 = 65.5) |
| 7 | 0, 2, 3, 5, 5, 8 | 6 students | 70, 72, 73, 75, 75, 78 | Contains Median Q2 (Median = 78) |
| 8 | 0, 1, 2, 5, 8, 9 | 6 students | 80, 81, 82, 85, 88, 89 | Contains Q3 Boundary (Q3 = 89.5) |
| 9 | 0, 2, 4, 5, 6, 8 | 6 students | 90, 92, 94, 95, 96, 98 | Maximum Value Row (Max = 98) |
Step-by-Step Five-Number Summary & IQR Calculation
To calculate the 5-number summary and stem-and-leaf layout for the 25 exam scores:
Step 1 (Order Data Set): 52, 55, 58, 61, 64, 64, 67, 70, 72, 73, 75, 75, 78, 80, 81, 82, 85, 88, 89, 90, 92, 94, 95, 96, 98
Step 2 (Determine Minimum & Maximum): Minimum = 52, Maximum = 98
Step 3 (Calculate Median Q2): Sample size n = 25 &implies; Median is 13th ordered value &implies; Q2 = 78
Step 4 (Calculate First Quartile Q1): Lower half contains 12 values &implies; Average of 6th & 7th values &implies; Q1 = (64 + 67) ÷ 2 = 65.5
Step 5 (Calculate Third Quartile Q3): Upper half contains 12 values &implies; Average of 19th & 20th values &implies; Q3 = (89 + 90) ÷ 2 = 89.5
Step 6 (Calculate Interquartile Range IQR): IQR = Q3 - Q1 = 89.5 - 65.5 = 24.0 points
Thus, the dataset ranges from 52 to 98 points, centered at a median of 78 points, with a middle 50% spread (IQR) of 24.0 points.
Exploratory Graphics Comparison: Stem Plot vs. Histogram vs. Box Plot
Below is a comparative reference chart detailing when to use a Stem and Leaf Plot versus related exploratory graphics:
| Exploratory Graphic Type | Raw Value Preservation | Ideal Dataset Size | Primary Practical Application |
|---|---|---|---|
| Stem and Leaf Plot | YES (Preserves exact individual digits) | Small to Moderate (n < 100) | Classroom test scores, small clinical sample inspection. |
| Histogram | NO (Groups data into bin bars) | Large Datasets (n ≥ 100) | Continuous population distribution shape analysis. |
| Box Plot (Box and Whisker) | NO (Displays 5-number summary only) | Any Dataset Size | Comparing multiple group medians & identifying outliers. |
History & Mathematics: 1977 John Wilder Tukey & EDA
1977 John Wilder Tukey & Exploratory Data Analysis
In 1977, Princeton statistician John Wilder Tukey introduced the stem-and-leaf display in his seminal textbook Exploratory Data Analysis (EDA), revolutionizing statistical graphics by combining visual shape inspection with exact value retention.
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Frequently Asked Questions (FAQ)
What is a Stem and Leaf Plot key legend?
A key legend explains how to read the stem and leaf digits (e.g. Key: 7 | 2 = 72 means a stem of 7 and leaf of 2 represents the number 72).
What is a split-stem plot?
A split-stem plot divides each stem into two separate rows (the first row holds leaves 0–4 and the second holds leaves 5–9) to stretch out dense data and reveal subtle distribution details.
What is a back-to-back stem plot?
A back-to-back stem plot places two sets of leaves on opposite sides of a single central column of stems to visually compare two distributions (such as male vs. female test scores).