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Scatter Plots, Association, and Two-Way Tables
Students analyze relationships between two variables using scatter plots and two-way frequency tables.
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Beginner
15–20 minutes
Probability & Statistics
Probability & Statistics
Page 4 of 8
Inside Cover
Scatter Plots, Association, and Two-Way Tables
At a Glance
Binder SectionProbability & Statistics
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
What can a scatter plot show—and not show—about two variables?
Build Understanding
A scatter plot represents paired quantitative data. Describe direction, form, strength, clusters, and outliers. A positive association rises from left to right; a negative association falls.
Two-way tables organize paired categorical data. Compare conditional relative frequencies—not just counts—to decide whether categories appear associated.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Scatter plots use paired numerical data.
- Describe direction, form, strength, and outliers.
- Association does not prove causation.
- Two-way tables compare categorical variables.
- Relative frequencies make unequal groups comparable.
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Interactive Vocabulary
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Reveal one step at a time
Worked Examples
Example 1
Study time and score show an upward pattern
1
Positive association.
Example 2
Line of fit y=5x+60
1
At x=4, predict 80.
2
Treat as an estimate.
Ask and explain
Common Questions
Does every scatter plot need a line? No.
Can a strong association prove cause? No.
Why use percentages in a two-way table? They allow fair comparison of groups with different sizes.
Notice and correct
Common Misconceptions
Claiming association proves causation
Consider lurking variables and study design.
Extrapolating far beyond the data
Limit predictions to a reasonable domain.
Learn Through Video
Watch, pause, and explain
Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
A plot falls from left to right. Describe association.
2
We Do
Guided Practice
As study time rises and errors fall, association is negative.
Points close to an upward line show strong positive association.
A point far from the pattern is an outlier.
Compare row or column percentages consistently in a two-way table.
A lurking variable may help explain an observed association.
3
You Do
Independent Practice
A plot falls from left to right. Describe association.
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
Create a plausible data set with a strong association and one outlier. Compare a fit with and without the outlier.
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IXL
Interpret Scatter Plots
Open resourceDescribe Associations Using Scatter Plots
Open resourceTwo-Way Frequency Tables
Open resourceKhan Academy
Two-Variable Data
Open resourceDeltaMath
DeltaMath: Scatter Plots
Open resourceDeltaMath: Two-Way Tables
Open resource
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