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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.

What you'll learn

Why it matters: Marketing analysts use scatter plots to spot patterns between ad spend and sales, scientists use them to compare two measurements per subject, and athletes use them to track training hours versus performance.

Worked example

Problem. A scatter plot shows (hours studied, test score). As hours go up, score goes up. What kind of association is this?

  1. Both variables move in the same direction.
  2. That is a positive association.

Answer: Positive

Practice problems

1. Hours studied vs. test score, going up. Association?

Choices: Positive · Negative · None

Show solution
  1. Warm-up: First identify exactly what the question is asking: Hours studied vs. test score, going up. 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.

Answer: Positive

2. Outside temperature vs. hot-chocolate sales: as temp rises, sales fall. Association?

Choices: Positive · Negative · None

Show solution
  1. Warm-up: First identify exactly what the question is asking: Outside temperature vs. hot-chocolate sales: as temp rises, sales fall. Association?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. One up, the other down — negative.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Negative

3. Shoe size vs. IQ: random scatter. Association?

Choices: Positive · Negative · None

Show solution
  1. Warm-up: First identify exactly what the question is asking: Shoe size vs. IQ: random scatter. Association?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. No clear pattern means no association.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: None

4. Points roughly along a straight line indicate a:

Choices: Linear pattern · Nonlinear pattern

Show solution
  1. Core Practice: First identify exactly what the question is asking: Points roughly along a straight line indicate a:
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Straight-line shape = linear.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Linear pattern

5. Tighter cluster around a line shows:

Choices: Stronger correlation · Weaker correlation

Show solution
  1. Core Practice: First identify exactly what the question is asking: Tighter cluster around a line shows:
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Less scatter means a stronger linear relationship.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Stronger correlation

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