Lecture Notes: Types of Tables and Graphs

Overview

• Discussion on different types of tables and graphs.
• Some tables and graphs provide meaningful information while others can be misleading.

Frequency Polygon

• Uses line segments connected to points above class midpoint values.
• Plots a point for each class, unlike histograms which use bars.
• Relative Frequency Polygon: Uses relative frequency (proportions/percentages) instead.
• Key Features:
  • Heights correspond to class frequencies.
  • Line segments extend to the horizontal axis.
  • Can compare two sets of data on the same graph.

Example

• Steps to construct a frequency polygon:
  • Determine class midpoints.
  • Plot points for each class based on midpoints and frequencies.
  • Connect points with line segments.
  • Extend endpoints to the horizontal axis appropriately.

Misleading Graphs

• Non-zero Axis: Start axis at a non-zero point to exaggerate differences.
  • Example: Interest rates appear to increase rapidly when a graph starts at 3.14 instead of 0.
• Pictograph: Use of 2D/3D drawings to distort data representation.
  • Example: Candy collection comparison exaggerates difference using 3D graphics.

Scatterplot

• Plot of paired (x, y) quantitative data.
• Key Points:
  • Horizontal (x) and vertical (y) axes for respective variables.
  • Do not connect points with lines.

Time-Series Graph

• Used for quantitative data collected over time.
• Steps to construct:
  • Label horizontal axis with time.
  • Label vertical axis with data type (e.g., rainfall).
  • Plot points and connect them in order.

Stemplot

• Represents quantitative data by separating it into stem and leaf components.
• Back-to-Back Stemplot: Compare two data sets side by side.
• Benefits:
  • Retains original data values.
  • Shows data distribution shape.
  • Allows easy data comparison.

Bar Graph

• For qualitative or categorical data.
• Uses bars of equal width to show frequencies.
• Example: Survey of most frustrating sounds with categories like jackhammers, car alarms, etc.

Pie Chart

• Depicts categorical data as slices of a circle.
• Slice size proportional to category frequency.
• Construction can use relative frequency or degrees of a circle.
• Example: Create pie chart from survey data on frustrating sounds.

Conclusion

• Covered various types of graphs: frequency polygon, scatterplot, time-series graph, stemplot, bar graph, and pie chart.
• Discussed the potential for some graphs to be misleading.