2
3
4
5
2
7
4
1
3
8
23
45
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5
2
7
4
1
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8
23
45
The Stem and Leaf Plot Generator decomposes each data value into its stem (tens digit) and leaf (units digit), providing the fundamental building blocks for constructing a stem-and-leaf display. This classic statistical visualization, introduced by John Tukey, retains the original data values while showing the shape of the distribution.
For a two-digit number $$x$$, the decomposition is:
$$\text{Stem} = \left\lfloor \frac{x}{10} \right\rfloor, \quad \text{Leaf} = x - 10 \times \left\lfloor \frac{x}{10} \right\rfloor = x \mod 10$$
For example, the value 47 has stem 4 and leaf 7. The value 83 has stem 8 and leaf 3. Single-digit values (0-9) have stem 0.
To build a stem-and-leaf plot from the decomposed values:
For the dataset {23, 27, 38, 41, 45}, the plot would be:
$$\begin{array}{r|l} 2 & 3 \; 7 \\ 3 & 8 \\ 4 & 1 \; 5 \end{array}$$
The stem-and-leaf plot offers a unique advantage over histograms: it preserves the actual data values. While a histogram only shows frequency counts per bin, a stem-and-leaf plot lets you recover every original observation. This is particularly useful for small to moderate datasets (up to about 100 values).
The plot also serves as a quick sorting mechanism. Reading the stems and leaves from top to bottom, left to right, produces the sorted dataset. This makes it easy to identify the median, quartiles, and mode by visual inspection.
The shape of the leaves on each row reveals the distribution. A concentration of leaves in the middle stems suggests a bell-shaped distribution. Leaves clustered at high or low stems indicate skewness. Gaps in the stems may suggest bimodal or irregular distributions. The length of each leaf row corresponds to the frequency for that stem, functioning like a sideways histogram.
Enter five two-digit values (0-99). The calculator decomposes each value into its tens digit (stem) and units digit (leaf) using integer division and modular arithmetic. It also computes the minimum and maximum of the dataset.
Each stem-leaf pair reconstructs the original value: stem × 10 + leaf = value. Group the leaves by their stems to build the stem-and-leaf plot. Stems with more leaves represent more frequent ranges. The minimum and maximum help define the range of your data.
Inputs
Results
Stem 2: leaves 3, 7 | Stem 3: leaf 8 | Stem 4: leaves 1, 5. Range = 45 - 23 = 22.
Inputs
Results
Stem 5: leaves 1, 5, 8 | Stem 6: leaves 2, 7. Most values are in the 50s.
A stem-and-leaf plot is a data visualization that splits each value into a stem (leading digit) and a leaf (trailing digit). Stems are listed vertically and leaves are written horizontally next to their corresponding stem, creating a display that shows both the data distribution shape and the individual values.
Each row represents a stem value. The leaves on that row, when appended to the stem, give the original data values. For example, a stem of 3 with leaves 2, 5, 8 represents the values 32, 35, and 38. The length of each row shows the frequency for that range.
Unlike a histogram, a stem-and-leaf plot preserves the exact data values, allows quick identification of individual observations, and automatically sorts the data. It is particularly useful for small datasets where retaining individual values matters.
Yes, but the convention changes. For three-digit numbers, the stem is typically the hundreds and tens digits, and the leaf is the units digit. For example, 347 would have stem 34 and leaf 7. This calculator handles two-digit values (0-99) for simplicity.
A back-to-back stem-and-leaf plot places two datasets on either side of a shared stem column. One dataset's leaves extend to the left and the other's to the right. This allows direct visual comparison of two distributions sharing the same scale.
Stem-and-leaf plots work best for small to moderate datasets (roughly 10 to 100 values) where preserving individual data points is important. For larger datasets, histograms or density plots are more practical since the plot becomes too wide to read comfortably.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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