Visual Presentations for Continuous Data: Stem and Leaf Plots & Box Plots

Overview

• Discussed different visual presentation tools for continuous data: stem and leaf plots, and box plots.
• Emphasis on box plots due to their usefulness and frequent use in the course.

Stem and Leaf Plots

• Definition: Similar to histograms but turned on their side; allows identification of individual values.
• Components:
  • Stems: Numbers on the left side before the vertical dash line representing bins of fixed width.
  • Leaves: Individual numbers on the right side representing single observations.
  • Example: A stem "8." and leaf "9" corresponds to a value of 89 mmHg.
  • Repeated stems: Indicates splitting of ranges (e.g., 90-94, 95-99).

Box Plots

• Purpose: Insights into distribution, skewness, and outlying values; effective for comparing data across multiple groups.
• Components:
  • Box: Contains the middle 50% of data (IQR - 25th to 75th percentile).
  • Median Line: Middle line inside the box representing the 50th percentile (median).
  • Whiskers: Lines extending from the box showing the range of non-outlying values (smallest to largest non-outlier).
  • Outliers: Points beyond whiskers representing extreme values.

Example: Blood Pressure Data

• Box Plot: Balanced and symmetric, indicating symmetric distribution around the median.
• Interpretation:
  • Median, 25th, and 75th percentiles are displayed distinctly.
  • Whiskers indicate non-outlier min and max.

Example: Hospital Discharge Data

• Histogram: Right-skewed with more small values and few extremes.
• Box Plot Characteristics:
  • Skewed median closer to 25th percentile; extreme values represented as outliers.
  • Whiskers represent non-outliers and outliers shown as separate dots.
• Stem and Leaf Plot: Not efficient for large skewed data like this example with 1000 records.

Comparing Groups with Box Plots

• Side-by-Side Comparison:
  • Easier to compare distributions between groups (e.g., males vs. females).
  • Shows similarities and differences in medians, percentiles, and outliers effectively.

Key Insights:

• Box plots offer a clearer side-by-side comparison for multiple groups compared to histograms.
• Useful for visualizing data trends, spread, and identifying outliers.