Understanding Stem-and-Leaf Plots

A stem-and-leaf plot is a data visualization method that organizes numerical data to show its distribution. Each number is split into a "stem" (leading digits) and a "leaf" (trailing digits). For example, in the number 43, the stem is 4, and the leaf is 3. This layout allows you to quickly identify data clusters, gaps, and spread.

Interpreting the Plot

Each row represents data values that share the same "stem." The leaves extend horizontally and display individual values within that stem group. A higher density of leaves in a row indicates more frequent occurrences within that range, helping you identify modes, symmetry, and skewness in the data.

Using Tukey’s Fence for Outlier Detection

Outliers are identified using Tukey’s Fence, which relies on the Interquartile Range (IQR) to find values that fall significantly outside the typical data range. The process is as follows:

• Calculate the first quartile (Q1) and the third quartile (Q3) of the data.
• Find the IQR by subtracting Q1 from Q3 (IQR = Q3 - Q1).
• Define the "fences" to identify outliers:
  • Lower Fence: Q1 - 1.5 * IQR
  • Upper Fence: Q3 + 1.5 * IQR
• Values falling outside these fences are flagged as outliers, highlighted in the stem-and-leaf plot for easy identification. You can use the toggle above to exclude outliers from the analysis.

Practical Tips

• Data Clusters: Look for rows with dense groups of leaves, which indicate high frequencies in those ranges.
• Outliers: Outliers are highlighted in the plot. You can exclude them if they distort your analysis by toggling the "Exclude Outliers" checkbox.
• Symmetry and Spread: A balanced plot suggests symmetric data, while skewed leaves on one side indicate an asymmetric distribution.

Further Reading

For more insights into data visualization and statistical analysis, consider exploring the following topics:

• Stem-and-leaf display on Wikipedia
• Explore more calculators and visualation tools on the Research Scientist Pod