Relative Frequency Formulas in Two-Way Tables
Relative frequency formulas in two-way tables is a Grade 11 Algebra 1 statistics skill from enVision Chapter 11 with three distinct calculations. Joint relative frequency divides a cell count by the grand total: 15/100 = 0.15. Marginal relative frequency divides a row or column total by the grand total: 40/100 = 0.40. Conditional relative frequency divides a cell count by its row or column total: 15/40 = 0.375. These three formulas convert raw counts into proportions that are easier to compare across groups and reveal relationships between categorical variables.
Key Concepts
Joint relative frequency: $\frac{\text{joint frequency}}{\text{total frequency}}$.
Marginal relative frequency: $\frac{\text{marginal frequency}}{\text{total frequency}}$.
Common Questions
What is joint relative frequency?
A cell frequency divided by the grand total. It shows what fraction of all survey respondents fall into both categories simultaneously.
What is marginal relative frequency?
A row or column total divided by the grand total. It shows the proportion of all data in a specific category, regardless of the other variable.
What is conditional relative frequency?
A cell frequency divided by its row or column total. It shows the proportion within a subgroup — conditioned on one variable being fixed.
A cell shows 15 students, row total is 40, grand total is 100. Calculate all three frequencies.
Joint: 15/100 = 0.15. Marginal for the row: 40/100 = 0.40. Conditional: 15/40 = 0.375.
When should you use conditional vs joint relative frequency?
Use conditional when comparing within a subgroup (e.g., what fraction of boys chose option A?). Use joint when comparing across all respondents.
What is the denominator for conditional relative frequency?
The row total or column total, depending on which variable you are conditioning on — not the grand total.