Scatter Plots and Bivariate Data
Grade 8 · Math · Study Guide
Analyze relationships between two variables using scatter plots, trend lines, and correlation.
Bivariate data involves two variables measured on the same subject — like hours studied and test score. Scatter plots display this data as points on a coordinate plane, letting us see patterns at a glance.
When points tend to rise together, there is a positive association. When one increases as the other decreases, that is a negative association. When the points show no pattern, there is no association. We also describe strength: strong (tightly clustered near a line) or weak (spread out).
A line of best fit (trend line) captures the trend and lets us make predictions. But remember: correlation is not causation. Just because two variables are related does not mean one causes the other. Ice cream sales and drowning rates are both higher in summer, but ice cream does not cause drowning.
| Association | Pattern | Real-world Example |
|---|---|---|
| Positive (strong) | Points tightly cluster on upward line | Height vs. weight |
| Positive (weak) | Points loosely trend upward | TV hours vs. electricity bill |
| Negative (strong) | Points tightly cluster on downward line | Exercise vs. resting heart rate |
| None | No pattern | Shoe size vs. test score |
Key terms
- Bivariate Data
- Data involving two variables measured on the same subject.
- Scatter Plot
- A graph showing bivariate data as individual points on a coordinate plane.
- Positive Association
- Both variables increase together — the scatter plot trends upward.
- Negative Association
- One variable increases as the other decreases — the plot trends downward.
- Line of Best Fit
- A line drawn through data representing the trend; used for predictions.
- Outlier
- A data point far from the overall pattern of the scatter plot.
Flashcards
- Scatter plot
- A graph of ordered pairs showing the relationship between two variables.
- Positive association
- Both variables increase together; scatter plot trends upward.
- Negative association
- One increases as the other decreases; plot trends downward.
- No association
- No clear pattern; variables appear unrelated.
- Line of best fit
- Line through data representing the trend; used for predictions.
- Correlation is not causation
- Related variables may not have a cause-effect relationship.
Practice questions
As x increases, y also increases. This is a ___ association.
- Negative
- No
- Positive
- Neutral
Show answer
Answer: Positive
When both variables increase together, it is a positive association.
A line of best fit must pass through every data point.
Show answer
Answer: False
A line of best fit balances above and below points — it does not pass through every point.
A data point far from the overall pattern is called an ___.
Show answer
Answer: outlier
An outlier falls far from the general pattern and can skew the trend line.
Line of best fit: y = 2x + 10. Predict y when x = 7.
- 17
- 20
- 24
- 38
Show answer
Answer: 24
y = 2(7) + 10 = 14 + 10 = 24.
Correlation between two variables proves one causes the other.
Show answer
Answer: False
Correlation shows association, not causation. Other factors may explain the relationship.
Fun facts
- There is a near-perfect correlation between per-capita cheese consumption and deaths by bedsheet tangling. This is a perfect example of why correlation does not equal causation.
- The line of best fit is also called a regression line — the same math used in weather forecasting and stock market analysis.
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