Statistics and Probability Foundations
What this domain tests
Statistics and Probability Foundations tests descriptive summaries, common distributions, correlation, sampling methods and basic probability rules. Expect calculation questions and interpretation questions where the wording matters.
Core rules and concepts
- Central tendency: mean, median, mode. Spread: range, variance, standard deviation, IQR. Use the median for skewed data.
- Distributions: normal is bell-shaped and symmetric; binomial counts successes in fixed trials; uniform gives equal likelihood. A z-score is z = (x - mean) / standard deviation.
- Correlation r lies between -1 and 1. The sign gives direction and the size gives strength. Correlation is not causation.
- Sampling: simple random, stratified (preserves groups), systematic and cluster. Larger random samples reduce sampling error. The central limit theorem says sample means tend toward a normal distribution.
- Probability: P(A or B) = P(A) + P(B) - P(A and B). For independent events, P(A and B) = P(A)P(B). Conditional probability P(A|B) = P(A and B) / P(B).
Worked example
In a class of 40, 24 like AI, 16 like data science, and 8 like both. P(AI or DS) = 24/40 + 16/40 - 8/40 = 32/40 = 0.8. P(AI|DS) = 8/16 = 0.5. Reasoning: the 8 students counted twice must be subtracted once, and conditional probability restricts the denominator to the 16 data-science likers.
Traps that cost marks
Do not use the mean when outliers dominate. Correlation 0 does not mean no relationship; it means no linear relationship. Do not confuse stratified sampling with cluster sampling. Independent events are not the same as mutually exclusive events. Distinguish sample statistics from population parameters.