Statistics and Probability
Statistics and Probability
This domain tests data analysis (shape, center, spread, displays), study design and sampling, probability rules, conditional probability, and expected value, including the normal distribution and regression. Expect questions that require interpreting a result, not just calculating one.
Core rules and concepts
- Center and spread: mean and standard deviation are sensitive to outliers; median and IQR are resistant. Skew pulls the mean toward the tail.
- Normal distribution: about 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD; use z = (x − μ)/σ.
- Probability: 0 ≤ P(A) ≤ 1; P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A|B) = P(A ∩ B)/P(B).
- Independence: P(A ∩ B) = P(A)P(B). Mutually exclusive events cannot co-occur, so P(A ∩ B) = 0.
- Sampling: random selection reduces bias; larger samples reduce variability but not bias.
Worked example
At a school, 40% of students take science, 60% take math, and 25% take both. Find P(math | science). P(math | science) = P(math ∩ science)/P(science) = 0.25/0.40 = 0.625. So 62.5% of science students also take math. Reasoning: the condition restricts the sample space to science students, so divide the overlap by the science total, not by the math total.
Traps that cost marks
- Confusing P(A|B) with P(B|A) (the "transposed conditional").
- Treating independent events as mutually exclusive, or vice versa.
- Reading a two-way table's margins as joint probabilities.
- Adding standard deviations instead of variances when combining independent variables.