Stem-and-Leaf Plot

Introduction to Stem-and-Leaf Plots

A stem-and-leaf plot is a visualization chart used to display data distribution that retains original data information while intuitively showing the distribution shape. The stem-and-leaf plot organizes and displays data by decomposing it into “stems” (higher-order digits) and “leaves” (lower-order digits).

Stem-and-leaf plots differ from histograms in that stem-and-leaf plots preserve the specific values of each data point, while histograms only show the frequency of data falling within intervals. Stem-and-leaf plots are particularly suitable for small to medium-sized datasets, as they can simultaneously display distribution shape, central tendency, and specific values.

When comparing the distribution of two groups of data, back-to-back bilateral stem-and-leaf plots can be used to clearly contrast the distribution characteristics of the two datasets.

English Name: Stem-and-Leaf Plot, Stem-and-Leaf Diagram

Components of Stem-and-Leaf Plots

Single-Direction Stem-and-Leaf Plot

Chart Type	Single-Direction Stem-and-Leaf Plot
Suitable Data	List: A set of continuous numerical data
Function	Display data distribution shape while preserving original data information
Data-to-Visual Mapping	High-order digits of values serve as stems (arranged vertically) Low-order digits of values serve as leaves (arranged horizontally) Each row represents all data with the same stem value
Suitable Data Size	20-100 data points; other visualization methods are recommended for larger datasets

Bilateral Stem-and-Leaf Plot

Chart Type	Bilateral Stem-and-Leaf Plot
Suitable Data	List: Two sets of continuous numerical data
Function	Compare distribution shapes and characteristics of two datasets
Data-to-Visual Mapping	Shared stems (arranged vertically in the center) Left group data leaves arranged to the left Right group data leaves arranged to the right Different data groups distinguished by color
Suitable Data Size	20-50 data points per group

Components:

Stem: High-order digits of data, arranged vertically in the center of the chart
Leaf: Low-order digits of data, arranged horizontally on both sides of the stem
Separator Line: Vertical line separating left and right data groups
Title/Legend: Identifies the meaning of different data groups
Data Sorting: Leaves are typically arranged from small to large

Application Scenarios for Stem-and-Leaf Plots

Suitable Scenarios

1. Basic Single-Direction Stem-and-Leaf Plot - Displaying Single Group Data Distribution

Single-direction stem-and-leaf plots are suitable for displaying the distribution of a single group of data, clearly showing central tendency and distribution shape.

Example: Student Exam Score Distribution

The chart below shows the mathematics score distribution of a class:

Student Scores
65, 67, 69, 71, 72, 73, 74, 75, 76, 78, 79, 81, 82, 83, 85, 87, 89, 92, 93, 95

import { Chart } from '@antv/g2';

const chart = new Chart({
  container: 'container',
  autoFit: true,
});

// Single group data
const rawData = [
  65, 67, 69, 71, 72, 73, 74, 75, 76, 78, 79, 81, 82, 83, 85, 87, 89, 92, 93, 95,
];

// Process single-direction stem-and-leaf plot data
function processSingleStemLeaf(data) {
  const stemMap = new Map();

  data.forEach((score) => {
    const stem = Math.floor(score / 10);
    const leaf = score % 10;
    if (!stemMap.has(stem)) {
      stemMap.set(stem, []);
    }
    stemMap.get(stem).push(leaf);
  });

  // Sort leaves
  Array.from(stemMap.values()).forEach((leaves) => {
    leaves.sort((a, b) => a - b);
  });

  const stems = Array.from(stemMap.keys()).sort((a, b) => b - a); // Sort from large to small
  const chartData = [];

  stems.forEach((stem, index) => {
    const yPos = index;
    const leaves = stemMap.get(stem);

    // Add stem
    chartData.push({
      x: 0.4,
      y: yPos,
      text: `${stem}`,
      type: 'stem',
      fill: '#333',
      fontSize: 18,
      fontWeight: 'bold',
    });

    // Add leaves
    leaves.forEach((leaf, i) => {
      chartData.push({
        x: 0.47 + i * 0.04,
        y: yPos,
        text: `${leaf}`,
        type: 'leaf',
        fill: '#1890ff',
        fontSize: 14,
        fontWeight: 'normal',
      });
    });
  });

  return { chartData, maxY: stems.length };
}

const { chartData, maxY } = processSingleStemLeaf(rawData);

chart.options({
  type: 'view',
  data: chartData,
  children: [
    {
      type: 'text',
      encode: {
        x: 'x',
        y: 'y',
        text: 'text',
        fill: 'fill',
        fontSize: 'fontSize',
        fontWeight: 'fontWeight',
      },
      style: {
        textAlign: 'center',
        textBaseline: 'middle',
      },
    },
    // Add separator line using lineX method
    {
      type: 'lineX',
      data: [0.45],
      style: {
        lineWidth: 1,
        stroke: '#333',
        strokeOpacity: 0.6,
      },
    },
  ],
  scale: {
    x: { domain: [0, 1], nice: false },
    y: { domain: [-0.5, maxY - 0.5], nice: false },
  },
  axis: false,
});

chart.render();

Explanation:

Stems represent the tens digit of scores (6, 7, 8, 9)
Leaves represent the ones digit of scores, arranged in ascending order
The chart shows that scores are mainly concentrated in the 70-80 range

2. Bilateral Stem-and-Leaf Plot - Comparing Two Group Data Distributions

Bilateral stem-and-leaf plots are particularly suitable for comparing distribution differences between two groups of data, intuitively showing the relative positions and distribution characteristics of both groups.

Example: Comparing Exam Score Distributions of Two Classes

The chart below shows a comparison of exam score distributions between Class A and Class B:

Data Group	Score Range
Class A	45-78
Class B	43-82

import { Chart } from '@antv/g2';

const chart = new Chart({
  container: 'container',
  autoFit: true,
});

const rawData = {
  left: [
    45, 47, 48, 52, 53, 55, 56, 57, 59, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72,
    73, 74, 75, 76, 77, 78,
  ],
  right: [
    43, 44, 46, 51, 54, 55, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 72, 73, 74,
    75, 76, 77, 79, 82,
  ],
};

// Process bilateral stem-and-leaf plot data
function processDualStemLeaf(data) {
  const stemMap = new Map();

  ['left', 'right'].forEach((side) => {
    data[side].forEach((score) => {
      const stem = Math.floor(score / 10);
      const leaf = score % 10;
      if (!stemMap.has(stem)) {
        stemMap.set(stem, { left: [], right: [] });
      }
      stemMap.get(stem)[side].push(leaf);
    });
  });

  // Sort
  Array.from(stemMap.values()).forEach((group) => {
    group.left.sort((a, b) => b - a); // Left side descending
    group.right.sort((a, b) => a - b); // Right side ascending
  });

  const stems = Array.from(stemMap.keys()).sort((a, b) => b - a); // Stems from large to small
  const chartData = [];

  stems.forEach((stem, index) => {
    const yPos = index;
    const { left, right } = stemMap.get(stem);

    // Add stem
    chartData.push({
      x: 0.5,
      y: yPos,
      text: `${stem}`,
      type: 'stem',
      fill: '#333',
      fontSize: 18,
      fontWeight: 'bold',
    });

    // Add left leaves (Class A)
    left.forEach((leaf, i) => {
      chartData.push({
        x: 0.45 - (i + 1) * 0.035,
        y: yPos,
        text: `${leaf}`,
        type: 'leaf-left',
        fill: '#1f77b4',
        fontSize: 14,
        fontWeight: 'normal',
      });
    });

    // Add right leaves (Class B)
    right.forEach((leaf, i) => {
      chartData.push({
        x: 0.55 + i * 0.035,
        y: yPos,
        text: `${leaf}`,
        type: 'leaf-right',
        fill: '#ff7f0e',
        fontSize: 14,
        fontWeight: 'normal',
      });
    });
  });

  // Add titles
  chartData.push({
    x: 0.35,
    y: stems.length,
    text: 'Class A',
    type: 'title',
    fill: '#1f77b4',
    fontSize: 16,
    fontWeight: 'bold',
  });

  chartData.push({
    x: 0.65,
    y: stems.length,
    text: 'Class B',
    type: 'title',
    fill: '#ff7f0e',
    fontSize: 16,
    fontWeight: 'bold',
  });

  return { chartData, maxY: stems.length + 1 };
}

const { chartData, maxY } = processDualStemLeaf(rawData);

chart.options({
  type: 'view',
  data: chartData,
  children: [
    {
      type: 'text',
      encode: {
        x: 'x',
        y: 'y',
        text: 'text',
        fill: 'fill',
        fontSize: 'fontSize',
        fontWeight: 'fontWeight',
      },
      style: {
        textAlign: 'center',
        textBaseline: 'middle',
      },
    },
    {
      type: 'lineX',
      data: [{ x: 0.47 }, { x: 0.53 }],
      encode: {
        x: 'x',
      },
      style: {
        lineWidth: 2,
        stroke: '#000',
        strokeOpacity: 0.8,
      },
    },
  ],
  scale: {
    x: { domain: [0, 1], nice: false },
    y: { domain: [-0.5, maxY - 0.5], nice: false },
  },
  axis: false,
});

chart.render();

Explanation:

Stems represent the tens digit of scores, shared and displayed in the center
Left leaves represent Class A students’ ones digits, arranged in descending order
Right leaves represent Class B students’ ones digits, arranged in ascending order
Colors distinguish between the two classes’ data
Clearly compares the score distribution differences between the two classes

3. Grouped Stem-and-Leaf Plot - Displaying Multiple Category Data

When comparing data distributions across multiple categories, grouped stem-and-leaf plots can be used.

Example: Height Distribution Across Different Age Groups

The chart below shows height distributions for three age groups: teenagers, adults, and elderly:

import { Chart } from '@antv/g2';

const chart = new Chart({
  container: 'container',
  autoFit: true,
});

const ageGroupData = {
  Teenagers: [155, 158, 160, 162, 165, 167, 168, 170, 172, 175],
  Adults: [160, 163, 165, 168, 170, 172, 175, 177, 180, 182, 185],
  Elderly: [150, 155, 158, 160, 162, 165, 167, 168, 170, 172],
};

// Process grouped stem-and-leaf plot data
function processGroupedStemLeaf(data) {
  const groups = Object.keys(data);
  const colors = ['#1f77b4', '#ff7f0e', '#2ca02c'];
  const chartData = [];
  let currentY = 0;

  groups.forEach((group, groupIndex) => {
    const groupData = data[group];
    const stemMap = new Map();

    // Add group title
    chartData.push({
      x: 0.1,
      y: currentY,
      text: group,
      type: 'group-title',
      fill: colors[groupIndex],
      fontSize: 16,
      fontWeight: 'bold',
    });
    currentY += 0.5;

    // Process data
    groupData.forEach((height) => {
      const stem = Math.floor(height / 10);
      const leaf = height % 10;
      if (!stemMap.has(stem)) {
        stemMap.set(stem, []);
      }
      stemMap.get(stem).push(leaf);
    });

    // Sort leaves
    Array.from(stemMap.values()).forEach((leaves) => {
      leaves.sort((a, b) => a - b);
    });

    const stems = Array.from(stemMap.keys()).sort((a, b) => a - b);

    stems.forEach((stem) => {
      const leaves = stemMap.get(stem);

      // Add stem
      chartData.push({
        x: 0.2,
        y: currentY,
        text: `${stem}`,
        type: 'stem',
        fill: '#333',
        fontSize: 14,
        fontWeight: 'bold',
      });

      // Add leaves
      leaves.forEach((leaf, i) => {
        chartData.push({
          x: 0.27 + i * 0.03,
          y: currentY,
          text: `${leaf}`,
          type: 'leaf',
          fill: colors[groupIndex],
          fontSize: 12,
          fontWeight: 'normal',
        });
      });

      currentY += 1;
    });

    currentY += 0.5; // Space between groups
  });

  return { chartData, maxY: currentY };
}

const { chartData, maxY } = processGroupedStemLeaf(ageGroupData);

chart.options({
  type: 'view',
  data: chartData,
  children: [
    {
      type: 'text',
      encode: {
        x: 'x',
        y: 'y',
        text: 'text',
        fill: 'fill',
        fontSize: 'fontSize',
        fontWeight: 'fontWeight',
      },
      style: {
        textAlign: 'left',
        textBaseline: 'middle',
      },
    },
    // Add separator line using lineX method
    {
      type: 'lineX',
      data: [0.25],
      style: {
        lineWidth: 1,
        stroke: '#333',
        strokeOpacity: 0.6,
      },
    },
  ],
  scale: {
    x: { domain: [0, 1], nice: false },
    y: { domain: [0, maxY], nice: false },
  },
  axis: false,
});

chart.render();

Explanation:

Data is grouped and displayed by age group
Each group uses different colors for distinction
Clearly compares height distribution characteristics across different age groups
Suitable for displaying distribution comparisons of multiple category data

Unsuitable Scenarios

Example 1: Cases with excessive data volume

When data volume exceeds 100 points, stem-and-leaf plots become too crowded and difficult to read. In such cases, histograms or box plots are recommended.

Example 2: Cases with excessive data range

When data spans a very large range (e.g., from 1 to 10,000), the number of stems becomes excessive, making the chart overly long. It’s recommended to group or transform the data appropriately first.

Example 3: Scenarios requiring precise numerical comparison

Although stem-and-leaf plots preserve original data, when precise numerical calculations and comparisons are needed, tabular format may be more suitable.

Comparison with Other Charts

Stem-and-Leaf Plots vs Histograms

Stem-and-Leaf Plots: Preserve specific values of each data point, showing both distribution shape and data integrity, but only suitable for small to medium-sized datasets
Histograms: Display data distribution through grouped intervals, can handle large amounts of data, but lose specific numerical information of original data

Stem-and-Leaf Plots vs Box Plots

Stem-and-Leaf Plots: Show complete data distribution shape and each data point, convenient for identifying data patterns and specific positions of outliers
Box Plots: Display statistical characteristics of data distribution through five-number summary (minimum, Q1, median, Q3, maximum), more concise but with limited information

Stem-and-Leaf Plots vs Scatter Plots

Stem-and-Leaf Plots: Focus on displaying single variable distribution, organizing data in an orderly manner through stem-leaf structure
Scatter Plots: Display relationships and correlations between two variables, more suitable for exploring association patterns between variables

Similar Charts

Histogram Chart

ComparisonDistribution

Box Plot

DistributionComparison

Scatter Plot

Distribution