A stem and leaf plot is a data visualization method that displays quantitative data while preserving the individual values. Each data value is split into a "stem" (usually the first digit or digits) and a "leaf" (usually the last digit).

For example, in a set of two-digit numbers like 42, 47, 36, 51:

• The stem would be the tens digit (4, 4, 3, 5)
• The leaf would be the ones digit (2, 7, 6, 1)
• This would be displayed as:

3 | 6
4 | 2 7
5 | 1

Following the Wikipedia approach, the plot reads as:

Key: 3|6 = 36

Data transformations are useful when your data has:

• Very large numbers: Use log₁₀ for numbers above 1000 to make them more manageable
• Wide range: When data spans multiple orders of magnitude (e.g., 10, 100, 1000, 10000)
• Skewed distribution: To make heavily skewed data more symmetric

Transformation examples:

• log₁₀(1000) = 3
• log₁₀(10000) = 4
• log₂(32) = 5
• ln(100) ≈ 4.6

When reading a stem and leaf plot:

• Each stem represents a group or class of data
• Each leaf shows the actual individual value within that class
• The shape reveals the distribution pattern (symmetric, skewed, bimodal)
• The density of leaves shows where data is concentrated
• Count the total number of leaves to get the sample size
• Find the median by counting (n+1)/2 leaves from either end

Example: In a plot with 25 values, the median would be the 13th value when counting from either end.

Back-to-back stem and leaf plots allow you to compare two datasets with the same stem values:

• Left side: First dataset leaves (right-aligned)
• Center: Stem values
• Right side: Second dataset leaves (left-aligned)

Ideal for comparing groups like test scores between classes, heights between genders, or performance before/after an intervention.