Grade 8 · Grade 8: Bivariate Data · Bivariate Data
Scatter Plots, Trend Lines and Two-Way Tables
Describe association in bivariate data, fit a line of best fit and read relative frequencies from two-way tables.
Learning objectives
- Construct and interpret scatter plots, describing clustering, outliers and association.
- Fit a line of best fit and interpret slope and intercept.
- Use two-way tables and relative frequencies to spot association.
- Distinguish association from causation.
AERO Mathematics alignment
AERO.M8.SP.1
Construct and interpret scatter plots for bivariate measurement data, describing patterns such as clustering, outliers, positive or negative association, and linear or non-linear association.
AERO.M8.SP.2
Know that straight lines model many bivariate relationships, informally fit a line of best fit and use the equation to solve problems, interpreting slope and intercept.
AERO.M8.SP.3
Understand that patterns of association in bivariate categorical data can be seen by displaying frequencies and relative frequencies in a two-way table.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion B — Investigating patterns
- Criterion C — Communicating
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
A student plots hours of study against test score for 20 classmates and sees the points drifting upward from left to right, with one point far off on its own.
Think about it
What does the upward drift suggest, and what should be done about the stray point?
Hint: Association is not the same as causation.
EXPLAIN
Scatter plots, trend lines and tables
Bivariate data records two measurements for each individual. A scatter plot shows one variable on each axis, revealing clustering, outliers and the direction and form of association.
| Pattern | What you see | Example |
|---|---|---|
| Positive association | Points rise to the right | Study time and score |
| Negative association | Points fall to the right | Car age and price |
| No association | A shapeless cloud | Shoe size and test score |
| Non-linear | A curve | Speed and stopping distance |
Line of best fit
A trend line summarises a linear pattern. Its slope is the predicted change in y for each unit increase in x; its intercept is the predicted value of y when x is zero — which is sometimes meaningless in context.
Two-way tables
For two categorical variables, a two-way table of frequencies becomes far more informative once you convert to relative frequencies within each row or column, because that reveals association even when the group sizes differ.
Common misconception
Correlation is not causation. Ice-cream sales and swimming accidents rise together, but the cause is hot weather.
INVESTIGATION
Try it yourself
Collect two measurements from 15 people, such as height and arm span. Draw a scatter plot, add a line of best fit by eye, write its equation and use it to predict one new value. State one reason your prediction could be wrong.
Interactive simulation · PhET
Least-Squares Regression
Place data points, draw your own line, then reveal the best-fit line and compare.
While you explore
- How close was your line to the least-squares line?
- What happens to the line when you add one extreme outlier?
Key vocabulary
- Outlier
- A value that sits far away from the rest.
- Line of best fit
- A straight line drawn to follow the trend of the points.
Practice questions
0/1 correct
Level 1 · Criterion A
A scatter plot of car age against price shows points falling to the right. What does this indicate?
MYP criterion tasks
Level 2 · Criterion D
A line of best fit is y = 4x + 55, where x is study hours and y is score. Interpret the slope and intercept, and state one limitation.
Reflect & track
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