Statistics and probability
What Statistics and probability tests
This domain tests describing data, modelling relationships, and quantifying uncertainty. Expect summary statistics, correlation and regression, probability rules, discrete random variables, and the binomial and normal distributions.
Core rules
- Center and spread: mean, median, quartiles, IQR and standard deviation. An outlier is often below Q_1 − 1.5 IQR or above Q_3 + 1.5 IQR.
- Regression: the least-squares line is ŷ = a + bx; r measures linear strength and direction, not causation.
- Probability: P(A∪B) = P(A) + P(B) − P(A∩B); mutually exclusive means P(A∩B) = 0; P(A|B) = P(A∩B)/P(B) for P(B)>0; independent means P(A∩B) = P(A)P(B).
- Binomial X ~ B(n,p): P(X = k) = C(n,k)p^k(1 − p)^(n−k), E(X) = np, Var(X) = np(1 − p).
- Normal X ~ N(μ,σ^2): standardize with z = (x − μ)/σ; use calculator normal functions and symmetry.
Worked example
Let X ~ B(10,0.3). Find P(X ≥ 1). Use the complement: P(X ≥ 1) = 1 − P(X = 0) = 1 − C(10,0)(0.3)^0(0.7)^10 = 1 − 0.7^10 ≈ 0.9718.
Traps
Reading at least one as P(X = 1); using P(B) instead of P(B|A) in a conditional; assuming mutually exclusive events are independent; using a regression line far outside the data; using σ^2 where σ is required.