Statistics and Probability: data, chance and inference
This domain covers the full data cycle and the main probability models: sampling methods and bias, data types, measures of centre and spread, box plots and outliers, Pearson's correlation coefficient and the least-squares regression line, probability with Venn and tree diagrams, discrete random variables and expected value, the binomial and normal distributions, and the chi-squared test.
Core rules
- A value is an outlier if it lies below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.
- Pearson's r lies between −1 and 1 and measures linear association only.
- The regression line ŷ = ax + b is found on the GDC; interpolation is inside the data range, extrapolation outside it.
- P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A|B) = P(A ∩ B)/P(B).
- E(X) = Σ x·P(x); binomial requires fixed n, constant p and independent trials.
- Chi-squared: degrees of freedom = (rows − 1)(columns − 1), expected frequencies should be at least 5.
Worked example
A machine produces defective items with probability 0.3, independently. For 12 items, find P(at least 2 defective). Use the complement: P(X ≥ 2) = 1 − P(X = 0) − P(X = 1) = 1 − 0.7¹² − 12(0.3)(0.7¹¹) = 1 − 0.01384 − 0.07118 = 0.915 (3 s.f.). Writing the event as "at least" is the signal to use the complement rather than summing ten terms.
Traps that cost marks
Claiming causation from a high r; extrapolating a regression line beyond the data; forgetting that r is unchanged by unit conversion; treating independent events as mutually exclusive; using binomial when p is not constant; reading a normal probability from the wrong tail; using the wrong degrees of freedom in chi-squared.