Lesson 11-4: Two-Way Tables

Property

A two-way frequency table displays the counts (frequencies) of data for two different categorical variables to summarize the relationship between them.

To construct a two-way table from raw data:

1. Identify the two categorical variables.
2. Create rows for categories of one variable and columns for categories of the other.
3. Tally each data point in the appropriate cell based on its category combination.
4. Record the frequency count for each cell intersection.

Examples

• Analyzing Survey Data: A survey asked students about their gender and their favorite sport. The results are organized into rows (Male, Female) and columns (Football, Basketball, Baseball).

• Sorting Raw Data: Raw data shows: 9th-Soccer: 8 students, 9th-Basketball: 5 students, 10th-Soccer: 6 students, 10th-Basketball: 9 students. You create a table with Grade Level as rows and Sport as columns, filling in these exact frequencies into the intersecting cells.

Property

For any row or column, the sum of the individual cell frequencies must equal the total for that row or column. A missing cell value can be found by subtracting the known cell values from the total.

Examples

Property

A two-way frequency table is accurate and consistent only if it satisfies three mathematical conditions:

1. Each row total equals the sum of the frequencies in that specific row.
2. Each column total equals the sum of the frequencies in that specific column.
3. The grand total equals the sum of all row totals, which must also equal the sum of all column totals.