Math Analysis & Approaches unit guide
Statistics and probability
Correlation and regression, probability, discrete and continuous random variables, binomial and normal distributions.
Statistics is the most GDC-dependent unit in AA and the one where Paper 2 marks are won or lost on calculator fluency rather than understanding. The distributions are all menu operations; what gets examined is whether you can tell which distribution a worded problem describes, and whether you set up the inequality the right way round. Students who practise reading questions rather than running calculations tend to find this the highest-scoring unit in the course.
Topics in this unit
What gets examined
- Choosing between binomial and normal from the description - fixed trials and two outcomes, or a continuous measurement.
- Normal distribution problems in both directions, including inverse normal to find a boundary value from a probability.
- Binomial probabilities for exactly, at most and at least, and translating each into calculator input.
- Expected value and variance for a discrete random variable from a probability distribution table.
- Correlation coefficient and regression line from data, and what r does and does not tell you.
- Conditional probability and independence, usually via a tree diagram or a Venn diagram.
How to revise it
Decide the distribution before touching the calculator
Counting successes in a fixed number of trials is binomial. A continuous measurement clustered around a mean is normal. Nearly every error here is the right method on the wrong distribution.
Rewrite "at least" as one minus "at most"
P(X >= 3) = 1 - P(X <= 2). Doing this conversion on paper before reaching for the GDC prevents the off-by-one that this topic is notorious for.
Know your inverse normal
Given a probability, find the value. It is a distinct menu operation from the forward direction and it appears every session. Practise until it is automatic.
Say what correlation does not mean
A strong r does not imply causation, and questions ask about this directly. One sentence, reliably available.
Where marks get lost
- Using P(X < 3) where P(X <= 3) was meant, which matters for a discrete variable and not for a continuous one.
- Extrapolating a regression line beyond the data and treating the result as reliable.
- Forgetting that probabilities in a distribution table must sum to one when solving for an unknown.
- Confusing the standard deviation with the variance in a normal calculation.
- Treating dependent events as independent in a tree diagram - the second branch changes.
Practise this unit
Reading about a unit only goes so far. Work through real IB-style questions on it, with mark schemes.