Grade 9 · Grade 9: Statistical Analysis and Probability · Statistical Analysis and Probability
Data Analysis, Regression and Conditional Probability
Compare distributions, fit and judge a regression line, and compute conditional probabilities.
Learning objectives
- Compare centre, spread and shape of two or more data sets, accounting for outliers.
- Fit a linear function to bivariate data and interpret slope and intercept.
- Compute and interpret the correlation coefficient and separate correlation from causation.
- Use two-way tables and Venn diagrams for conditional probability and independence.
AERO Mathematics alignment
AERO.M9.SP.1
Represent data with plots on the real number line and compare centre, spread and shape of two or more data sets, accounting for outliers.
AERO.M9.SP.2
Fit a linear function to bivariate data, interpret slope and intercept in context, compute and interpret the correlation coefficient, and distinguish correlation from causation.
AERO.M9.SP.3
Describe events as subsets of a sample space, and use two-way tables and Venn diagrams to compute conditional probabilities and test independence.
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 report claims that students who own more books score higher, with r = 0.78.
Think about it
What does that number actually justify saying?
Hint: Consider a hidden variable that affects both.
EXPLAIN
Comparison, regression and conditioning
Comparing distributions
Compare centre, spread and shape together, and say what happens when outliers are removed. Median and IQR are resistant to outliers; mean and standard deviation are not.
Regression and correlation
| r value | Strength | Direction |
|---|---|---|
| 0.9 to 1.0 | Very strong | Positive |
| 0.5 to 0.9 | Moderate to strong | Positive |
| about 0 | None | — |
| −0.5 to −1.0 | Moderate to very strong | Negative |
The regression line predicts y from x. Its slope is the predicted change in y per unit of x. Correlation measures only the strength of a linear pattern; it says nothing about cause, and a confounding variable such as family income can drive both variables at once.
Conditional probability
P(A | B) is the probability of A given that B has happened, calculated as P(A and B) ÷ P(B). Events A and B are independent when P(A | B) = P(A). Two-way tables make this easy to check row by row.
Common misconception
A high r never proves causation. Only a well-designed experiment with random assignment can support a causal claim.
INVESTIGATION
Try it yourself
Find a published claim linking two variables. Identify the correlation, propose one plausible confounding variable and describe an experiment that could test causation.
Watch
Exponential Growth and Decay Word Problems
Khan Academy · 7:21
Useful modelling context before you judge a regression line.
Before you watch: Does a strong correlation prove causation?
- Interpret r = −0.85.
- How do you test whether two events are independent using a two-way table?
Interactive simulation · PhET
Curve Fitting
Fit a line to data, read r, then add outliers and watch r change.
While you explore
- What does an r value of 0.9 tell you, and what does it not tell you?
- Can a strong correlation exist without causation? Give an example.
Key vocabulary
- Conditional probability
- The chance of something happening given that something else already has.
- Correlation coefficient
- A number showing how closely points follow a straight line.
Practice questions
0/1 correct
Level 1 · Criterion A
A study finds r = 0.82 between hours of sleep and test scores. What can be concluded?
MYP criterion tasks
Level 2 · Criterion D
In a class, 12 of 30 students play a sport and 8 of those 12 also play an instrument. Find P(instrument | sport) and explain.
Reflect & track
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