Integrated Math 1 / Unit 7: Descriptive Statistics
7.4 Two-Way Frequency Tables
Notes
A two-way table shows counts for two categorical variables.
- Joint frequencies are the counts in the cells. Marginal frequencies are the row and column totals.
- Conditional relative frequency: divide a cell by the row or column total that is given as the condition.
- Example: of 40 freshmen, 25 play a sport. Percent of freshmen who play $\displaystyle = \frac{25}{40} = 62.5\%$.
- If the conditional percents are about equal across groups, there is no association between the variables.
Practice
Among 100 students, 40 are freshmen and 60 are sophomores. 25 freshmen and 30 sophomores play a sport. What percent of freshmen play a sport?
$\displaystyle \frac{25}{40} = 0.625 = 62.5\%$.
Among 100 students, 40 are freshmen and 60 are sophomores. 25 freshmen and 30 sophomores play a sport. Of the students who play a sport, what percent are freshmen (to the nearest tenth)?
55 students play a sport, and $\displaystyle \frac{25}{55} \approx 0.455$.
Of 50 left-handed students, 20 play piano. Of 150 right-handed students, 60 play piano. What does this suggest?
$\displaystyle \frac{20}{50} = 40\%$ and $\displaystyle \frac{60}{150} = 40\%$.
Ready for more? Take the Unit 7 test.