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Understanding Various Graph Types

May 24, 2025

Lecture Notes: Graphs and Displays

Introduction

  • Focus on types of graphs and displays:
    • Stem and Leaf Plots
    • Dot Plots
    • Pie Charts
    • Pareto Charts
  • Scatter plots and time series plots discussed in another chapter.

Stem and Leaf Plots

  • Each number split into a stem and a leaf.
  • Similar to a histogram, retains original data values, and allows sorting of data.
  • Example:
    • Small data set: 26, 21, 25, 25, 26, 27, 28.
    • Stem for 26 is '2', leaf is '6'.
    • Leaves are written in numerical order.
  • Key Points:
    • Use rightmost digit as leaf; first digit as stem.
    • Key interpretation is crucial (e.g., 10/2 could mean 102 or 10.2).
    • Ensure no gaps (e.g., write '13' stem even if no data for 130-139).
    • Visual resemblance to a histogram when viewed sideways.
  • Practical use mainly for small data sets or quick pattern identification.

Dot Plots

  • Plots each data entry above a horizontal axis.
  • Example:
    • Horizontal axis from 20 to 45, dots placed for each data value.
    • Stack dots for repeating values.
  • Practical use is limited in real-world applications.
  • Identifies outliers easily (e.g., 145 as an outlier in text message data).

Pie Charts

  • Used for representing qualitative data as a whole.
  • Circle divided into sectors representing categories, proportional to frequency.
  • Example:
    • Degrees conferred in thousands (associates, bachelors, etc.).
    • Use central angle and relative frequency to construct pie chart.
    • Calculate angle by multiplying 360 degrees by category's relative frequency.
    • Relative frequencies often shown as percentages for clarity.
  • Can be created in Excel and StatCrunch.

Pareto Charts

  • Vertical bar graph with bar height representing frequency or relative frequency.
  • Bars arranged from tallest to shortest (left to right).
  • Deals with categorical data.
  • Example:
    • Leading causes of death in the U.S. organized from highest to lowest frequency.
  • Can be created in StatCrunch and Excel.

Conclusion

  • While some graphs like stem and leaf and dot plots are less common in professional settings, they are useful for educational and small data set purposes.
  • Pie and Pareto charts are more commonly seen in professional and real-world applications.