Cogito
Integrated Math 1 · Chapter 8 · Lesson 2
Two-Way Tables
Two categorical variables at once.
12 problems · about 20 minutes · S-ID.B.5
What this lesson teaches
The student reads two-way tables and computes relative frequencies to judge association.
- A two-way table cross-classifies by two categorical variables.
- Inner cells are joint counts; margins give each variable alone.
- Compare row proportions, never raw counts, to judge association.
Warm Up
Straightforward practice. Get the method working first.
5 problems9 yes out of 36. What proportion, as a decimal?
Answer 0.25
Why 0.25.
Why compare proportions rather than counts?
Answer The groups may be different sizes.
Why Unequal group sizes make counts misleading.
12 yes out of 48. Proportion as a decimal?
Answer 0.25
Why 12 ÷ 48.
Cells 20, 30, 25 and 25. Grand total?
Answer 100
Why Add all four.
A row has 20 yes and 30 no. Row total?
Answer 50
Why 20 + 30.
Build It Up
The same ideas with more to keep track of.
3 problemsThat row: proportion saying yes, as a decimal?
Answer 0.4
Why 20 ÷ 50.
Row proportions 0.5 and 0.5. Is there association? 1 yes, 0 no.
Answer 0
Why They match.
Row proportions 0.2 and 0.8. Is there association? 1 yes, 0 no.
Answer 1
Why They differ sharply.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each figure with where it comes from.
Answer Joint count → An inner cell of the table; Marginal total → A row or column total; Row relative frequency → A cell divided by its row total
Why Only one of these involves dividing.
18 yes out of 24. Proportion as a decimal?
Answer 0.75
Why 18 ÷ 24.
The Proportion: 30 yes out of 50. What proportion, as a decimal?
Answer 0.6
Why 0.6.
The Other Row: 15 yes out of 20. What proportion, as a decimal?
Answer 0.75
Why 0.75.