Two-Way Tables & Relative Frequency
Aligned to 8.SP.A.4 — Common Core State Standards for Mathematics.
What this lesson teaches
A two-way table organizes categorical data in rows and columns. Relative frequencies — dividing a cell by a row, column, or grand total — reveal whether the two variables are associated.
Worked examples
Example 1
Of 50 students, 30 own a pet, and of those 24 enjoy the animals class. The relative frequency is 24 ÷ 30 = 0.8, so 80% of pet owners enjoy the class. Comparing this to non-owners shows whether owning a pet is associated with enjoying the class.
Example 2
Of 20 students without a pet, 6 enjoy the animals class: 6 ÷ 20 = 30%. Compared with 80% of pet owners, there is a clear association.
Example 3
Compare within rows or within columns, not raw counts. A group with more members will show bigger counts even when its rate is lower.
Practice questions
- A two-way table shows 40 students in total; 18 are in the "walks to school" row. Find that row's relative frequency of the total.
- Out of 25 girls, 15 play a sport. What is the relative frequency?
- Explain how comparing relative frequencies can show an association between two categories.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Tablas de Doble Entrada y Frecuencia Relativa
Una tabla de doble entrada organiza datos categóricos en filas y columnas. Las frecuencias relativas — dividir una celda entre un total de fila, columna o general — revelan si las dos variables están asociadas.
Ejemplo 1: De 50 estudiantes, 30 tienen mascota, y de esos 24 disfrutan la clase de animales. La frecuencia relativa es 24 ÷ 30 = 0.8, así que el 80% de quienes tienen mascota disfruta la clase. Comparar esto con quienes no tienen mascota muestra si tener mascota está asociado con disfrutar la clase.
Ejemplo 2: De 20 estudiantes sin mascota, 6 disfrutan la clase de animales: 6 ÷ 20 = 30%. Comparado con el 80% de quienes tienen mascota, hay una asociación clara.
Ejemplo 3: Compara dentro de filas o de columnas, no conteos brutos. Un grupo con más integrantes mostrará conteos mayores aunque su tasa sea menor.
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