Lecture on Graphs for Interval and Ratio Level Data

Key Concepts

• Interval and Ratio Data: Both order and distance matter. Unlike ordinal data, distance in interval and ratio data is meaningful.
• Area in Graphs: A key takeaway is that area in graphs always means something.

Histograms

• Characteristics:
  • Bars in histograms touch because distance is meaningful.
  • Histogram bars represent continuous intervals, unlike bar graphs where distance doesn't matter and bars don't touch.
• Example:
  • Heights categorized in intervals (60-62 inches, 62-64 inches, etc.)
  • Can use raw frequency or relative frequency.
  • Important to understand that frequency can be converted to relative frequency.

Graph Construction

• X-axis and Y-axis:
  • X-axis represents the variable (e.g. height in inches).
  • Y-axis can represent percentages or raw numbers.
• Labeling:
  • Midpoints or endpoints of bars can be labeled; both are common practices.
  • Y-axis can show either relative frequency or frequency.

Bar Number and Width

• Bar Quantity: A good histogram usually has between 10 and 20 bars.
• Category Width: All categories should have equal width in a histogram.
  • If categories have unequal widths, it affects the meaning of area in graphs.

Common Mistakes

• Avoid having unequal width categories in histograms.
  • Incorrect representation leads to misleading area interpretations.
  • X-axis must accurately represent distance.

Density Histograms

• Definition: Used when categories have unequal widths.
  • Y-axis uses a density scale, representing percent per unit.
• Importance: Ensures area in the graph still accurately reflects data distribution.
• Application: More about understanding area importance rather than creating such graphs for general use.

Example of Density Scale

• Percent per Unit (PPU): If a bar is two units wide with 5% of people, it represents 2.5% per unit.
• Adjustments for unequal categories ensure areas still reflect actual distribution.

Importance of Area

• Area, not just height or width, determines the significance of sections in histograms.
• Essential for understanding probability distributions in future discussions.

Conclusion

• Understanding the properties and correct construction of histograms and density histograms is crucial.
• Emphasis on area meaning in graphs is important for future topics in probability distributions.

This concludes the lecture. The next session will cover further aspects of this topic.