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Scatter Plots and Trend Lines

A free Algebra I lesson from the “Statistics and Data Analysis” unit, with a worked example and practice problems including step-by-step solutions.

A scatter plot graphs paired data on two axes. The pattern shows the type and strength of the relationship: rising (positive), falling (negative), random (none); straight-line (linear) or curved (nonlinear); tightly clustered (strong) or spread out (weak). Even strong correlation does not prove that one variable causes the other. In Statistics and Data Analysis, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

What you'll learn

Why it matters: Marketing teams, public-health researchers, sports analysts, and quality engineers all use scatter plots to spot relationships before drawing conclusions about cause.

Worked example

Problem. A scatter plot of (hours studied, test score) rises to the right. What type of association is this?

  1. Both variables increase together.
  2. That is a positive association.
  3. Connect the result back to Scatter Plots and Trend Lines so the method and meaning are both clear.
  4. Check the result against the original representation before writing the final answer.

Answer: Positive

Practice problems

1. Hours practiced vs. free throws made (rising). Association?

Choices: Positive · Negative · None

Show solution
  1. Warm-up: First identify exactly what the question is asking: Hours practiced vs. free throws made (rising). Association?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Both increase together.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: Positive

2. Drink size vs. soda calories (rising). Association?

Choices: Positive · Negative · None

Show solution
  1. Warm-up: First identify exactly what the question is asking: Drink size vs. soda calories (rising). Association?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Bigger drinks have more calories.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: Positive

3. Ice-cream sales and drowning incidents both rise in summer. Does ice cream cause drowning?

Choices: Yes (causation) · No (just correlation)

Show solution
  1. Warm-up: First identify exactly what the question is asking: Ice-cream sales and drowning incidents both rise in summer. Does ice cream cause drowning?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. A third variable (hot weather) drives both.
  4. Correlation does not imply causation.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: No (just correlation)

4. Hours of TV vs. grades (falling). Association?

Choices: Positive · Negative · None

Show solution
  1. Core Practice: First identify exactly what the question is asking: Hours of TV vs. grades (falling). Association?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. More TV, lower grades — opposite directions.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: Negative

5. Random scatter with no pattern. Association?

Choices: Positive · Negative · None

Show solution
  1. Core Practice: First identify exactly what the question is asking: Random scatter with no pattern. Association?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. No discernible trend.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: None

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