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Graphical Methods for Quantitative Data

May 23, 2025

Lecture Notes: Graphical Representation for Quantitative Data

Stem and Leaf Plots (Stem Plots)

  • Purpose: Visual representation of quantitative data
  • Process:
    1. Split data values into stems and leaves
    2. Example: For the set of numbers from Georgia Southern University students:
      • Use the first digit as the stem and the second digit as the leaf
      • Example: 23 -> Stem: 2, Leaf: 3
      • For a dataset with decimals like 12.3 -> Stem: 12, Leaf: 3
    3. Write stems vertically and arrange leaves horizontally corresponding to the same stem
    4. Arrange leaves in increasing order
  • Deductions:
    • Show data center, variability, and identify symmetry or skewness
    • Techniques like splitting stems can provide better data visualization

Dot Plots

  • Purpose: Useful for small datasets
  • Process:
    1. Draw a horizontal axis
    2. Scale the axis from smallest to largest numbers in the dataset
    3. Represent each data point with a dot
  • Deductions:
    • Identify center and variability
    • Useful for identifying gaps and distribution shape

Scatter Plots

  • Purpose: Useful for paired data with coordinates
  • Process:
    1. Identify independent (explanatory) and dependent (response) variables
    2. Plot points on x (independent) and y (dependent) axes
    3. Do not connect the points
  • Deductions:
    • Identify relationships and trends (e.g., negative correlation)
    • Slope interpretation: Negative slope indicates one variable decreases as the other increases

Time Series Graphs (Line Graphs)

  • Purpose: Representation of data collected over time
  • Process:
    1. Plot data points over a time axis
    2. Connect consecutive points with line segments
    3. Do not connect to zero or extrapolate beyond data points
  • Deductions:
    • Identify trends, patterns, or anomalies over time
    • Useful for monitoring progress or changes, such as in dieting

Conclusion

  • Various graphical methods are available for representing quantitative data, each with specific use cases based on dataset size and data type
  • Important to choose the correct graph type based on the dataset characteristics and the insights needed

Test Preparation

  • Focus on identifying the appropriate graphical representation for different types of quantitative data
  • Be able to match graph types with appropriate data scenarios

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