AP Statistics study guide
AP Statistics · Work through your exam, one topic at a time.
AP Statistics is a College Board Advanced Placement course and exam that mirrors a one-semester, introductory, non-calculus-based college statistics course. It is designed for high school students who have completed a first-year algebra course and want college-level credit or placement while building skills they will use in news polls, medical research, AI models, and other data-rich fields. The AP Statistics study guide has 5 sections and about 1,667 words.
01Exploring One-Variable Data and Collecting Data
Always describe shape (roughly symmetric, skewed left/right, unimodal/bimodal, possible outliers), center (mean or median), and spread (range, IQR, standard deviation) - in that order. The mean is pulled toward skew and outliers; the median is resistant.
346 words, about 2 min02Probability, Random Variables, and Probability Distributions
Probabilities lie in [0, 1] and sum to 1 over a sample space. Use the complement rule P(Aᶜ) = 1 − P(A), the addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B), and the multiplication rule for independent events P(A ∩ B) = P(A)P(B).
317 words, about 2 min03Inference for Categorical Data: Proportions
Inference starts with a null hypothesis H₀ (typically p = p₀) and an alternative H₁ (one- or two-sided). A p-value is the probability, assuming H₀ is true, of observing a statistic at least as extreme as the one computed.
321 words, about 2 min04Inference for Quantitative Data: Means
When σ is unknown (always in practice), use the t-distribution with df = n − 1. It is symmetric and bell-shaped with heavier tails than normal, becoming normal as n grows.
330 words, about 2 min05Regression Analysis
A scatterplot is examined first for direction, form, strength, and outliers. The least-squares regression line ŷ = a + bx minimizes the sum of squared residuals; slope b = r(s y/s x) and intercept a = ȳ − b·x̄.
353 words, about 2 min