Scatter Plots and Bivariate Data
A free Pre-Algebra lesson from the “Statistics and Probability” unit, with a worked example and practice problems including step-by-step solutions.
A scatter plot graphs paired data — one variable on each axis — to look for a relationship. A positive association rises (both increase together); a negative association falls (one decreases as the other increases); no association looks like random scatter. Points clustered tightly around a single line show a strong correlation; loose cloud-like patterns are weak. In Statistics and Probability, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Identify positive, negative, and no association in scatter plots
- Distinguish linear from nonlinear patterns
- Compare strength of association by how tightly points cluster around a line
Worked example
Problem. A scatter plot shows (hours studied, test score). As hours go up, score goes up. What kind of association is this?
- Both variables move in the same direction.
- That is a positive association.
- Connect the calculation back to Scatter Plots and Bivariate Data so the method, not just the arithmetic, is clear.
- Check the result against the original question before writing the final answer.
Answer: Positive
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Hours studied vs. test score, going up. Association?
Choices: Positive · Negative · None
Show solution
- Both increase together.
Answer: Positive
2. Outside temperature vs. hot-chocolate sales: as temp rises, sales fall. Association?
Choices: Positive · Negative · None
Show solution
- One up, the other down — negative.
Answer: Negative
3. Shoe size vs. IQ: random scatter. Association?
Choices: Positive · Negative · None
Show solution
- No clear pattern means no association.
Answer: None
4. Points roughly along a straight line indicate a:
Choices: Linear pattern · Nonlinear pattern
Show solution
- Straight-line shape = linear.
Answer: Linear pattern
5. Tighter cluster around a line shows:
Choices: Stronger correlation · Weaker correlation
Show solution
- Less scatter means a stronger linear relationship.
Answer: Stronger correlation
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