AP Statistics 1.3 Representing a Categorical Variable with Tables Study Notes

Purpose of Tables:

• • To organize raw categorical data into a clear and interpretable format.
  • Helps identify patterns, compare categories, and prepare data for graphical representation (bar graphs, pie charts).
  • Summarizes large amounts of data in a compact structure.

Types of Tables for Categorical Data:

Frequency Table:

• • • Lists each category of the variable.
    • Shows the count (frequency) of observations that fall into each category.
    • Good for showing raw numbers but less useful for comparisons when sample sizes differ.

Relative Frequency Table:

• • • Lists each category along with the proportion (or percentage) of the total sample in that category.
    • Formula: \( \text{Relative Frequency} = \dfrac{\text{Category Frequency}}{\text{Total Frequency}} \)
    • Relative frequencies can be expressed as decimals, fractions, or percentages.
    • Useful for comparing distributions across groups of different sizes.

Cumulative Frequency Table:

• • • Shows the running total of frequencies up to a certain category.
    • More often used with ordered categorical or quantitative data.

Two-Way (Contingency) Table:

• • • Summarizes the relationship between two categorical variables.
    • Displays joint frequencies (counts of individuals that fall into a combination of categories).
    • Forms the basis for conditional relative frequencies and association analysis.

Steps in Creating a Frequency/Relative Frequency Table:

1. 1. Identify all unique categories of the variable.
   2. Count the number of individuals in each category (frequency).
   3. Compute relative frequency by dividing each frequency by the total number of observations.
   4. Verify that the sum of relative frequencies equals 1 (or 100%).

Key Advantages of Using Tables:

• • Organizes data systematically for analysis.
  • Relative frequency tables allow fair comparison between datasets of different sizes.
  • Provides the foundation for constructing graphs (bar graphs, pie charts, segmented bar charts).
  • Helps detect dominant and less common categories quickly.