Lesson 4: Categorical Data & Two-Way Tables

What is the difference between quantitative data and categorical data, and why do we use a two-way table to display the latter?

How do joint frequencies differ from marginal frequencies in a two-way table?

How does calculating relative frequencies (percentages or fractions) help us compare two groups of different sizes fairly?

What evidence in a relative frequency table suggests that an association exists between two categorical variables?

Categorical variable, Bivariate categorical data, Two-Way frequency table, Joint frequency, Marginal frequency, Relative frequency, Row/Column relative frequency, Pattern of association

CCSS.MATH.CONTENT.8.SP.A.4

Students pivot from quantitative data patterns (scatter plots) to categorical data structures. They learn to systematically organize survey data into two-way tables, summarize counts, and convert raw frequencies into relative percentages.

DOK Level: 3 (Strategic Thinking / Structural Analysis)

Confusing the Total Base: When calculating relative frequencies, students often divide by the grand total of the entire table instead of dividing by the specific row total or column total required by the question.

Frequency vs. Proportion: Mistaking a larger raw number (joint frequency) for a larger overall trend, ignoring the fact that the sample sizes of the groups being compared might be unequal.

Provide a "Two-Way Table Template" where the marginal total cells are visually highlighted or color-coded to help students map out where denominators come from.

Exit Tickets