Unit 1.3 – Representing a Categorical Variable with Tables
Why Tables?
**Tables** are a clear way to organize, display, and analyze data for categorical variables. They allow us to quickly see counts, percentages, and comparisons.
**Tables** are a clear way to organize, display, and analyze data for categorical variables. They allow us to quickly see counts, percentages, and comparisons.
🗂️ Types of Tables for Categorical Data
- Frequency Table: Shows number of cases in each category
- Relative Frequency Table: Shows proportion or percentage in each category
- Two-way (Contingency) Table: Shows how two categorical variables interact
Frequency Table Example
| Favorite Color | Count |
|---|---|
| Red | 12 |
| Blue | 8 |
| Green | 10 |
Relative Frequency Table Example
| Favorite Color | Percent |
|---|---|
| Red | 40% |
| Blue | 27% |
| Green | 33% |
📒 Anatomy of a Good Table
- Clear title describes what the table shows
- All categories are mutually exclusive (no overlaps)
- Includes all possible categories (even if zero!)
- Totals (count = n, percentages = 100%) always shown
🔑 Key Formula: Relative Frequency
\[
\text{Relative Frequency (proportion)} = \frac{\text{Count in Category}}{\text{Total Count}}
\]
\[
\text{Percentage in Category} = \frac{\text{Count in Category}}{\text{Total Count}} \times 100\%
\]
💡 Study Tips & Tricks
- Double-check row/column labels match the question and data
- Add “Other” category if needed for completeness
- Use bar charts to visualize frequency table results
- Report both counts and percentages for max clarity
- For two-way tables, always state which variable is the row and which is column
❌ Common Mistakes
- Not including every category (totals will be wrong!)
- Mixing up percent and proportions
- Leaving out totals (always show overall n or 100%)
- Rounding percentages so they don’t add to 100%
- Putting quantitative data (like scores) into a frequency table—should be grouped first
Summary:
Unit 1.3 covers how to represent a categorical variable with well-organized and correct tables: frequency tables, relative frequency tables, and two-way tables. Always show totals, be clear and organized, and know how to turn counts into proportions and percents!
Unit 1.3 covers how to represent a categorical variable with well-organized and correct tables: frequency tables, relative frequency tables, and two-way tables. Always show totals, be clear and organized, and know how to turn counts into proportions and percents!