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Library Catalogue AP Statistics
⁂   Mathematics · AP Exam

Statistics Study Library.

Expert-authored study guides, inference procedures, and original practice — covering all 9 units of AP Statistics from data exploration to regression inference.

9 units 40 MCQ + 6 FRQ 180 minutes 266,791 candidates (2025)
Total Time 180 minutes (3 hours)
MCQ 40 questions · 90 min · calculator OK
FRQ 6 5 short + 1 investigative task · 90 min
Score Scale 1–5 60.3% scored 3+ (2025)
Exam Structure

How the exam is scored.

Section I — Multiple Choice (50%)

40 questions · 90 minutes · calculator permitted throughout. Five answer choices (drops to four in 2027 revision). No penalty for wrong answers. Covers all 9 units.

Raw score: 1 point per correct answer (max 40), scaled to 50 composite points.

Section II — Free Response (50%)

Part A (Q1–5): Five multipart short-response questions, each scored 0–4. Q1 = data collection, Q2 = distributions, Q3 = probability, Q4 = inference, Q5 = combined skills.

Part B (Q6): One investigative task — a nonroutine, multi-part problem integrating multiple units, scored 0–4. Typically the lowest mean score of all six questions.

Formula Sheet Provided

A two-page official reference sheet is provided for the entire exam (both sections). It includes descriptive statistics, probability and distribution formulas, and all inferential statistics formulas. Three tables are also provided: Table A (standard normal), Table B (t-distribution), Table C (chi-square). Students must memorize conditions, test selection criteria, and proper contextual language — these do not appear on the formula sheet.

Score Distributions (2025)

5
17.3%
4
21.4%
3
21.6%
2
15.7%
1
24.0%

n = 266,791 · Mean score: 2.92 · 60.3% scored 3 or above

Curriculum

Study by unit.

1.
Exploring One-Variable Data
SOCS framework (shape, outliers, center, spread) · Categorical vs. quantitative variables · Dotplots, stemplots, histograms, boxplots · Mean, median, IQR, standard deviation · Outlier identification using $1.5 \times \text{IQR}$ rule · $z$-scores and standardization · Normal distribution: proportions and percentiles · Empirical rule (68–95–99.7%)
standard track
15–23% of exam
Study unit ›
2.
Exploring Two-Variable Data
DUFS framework (direction, unusual features, form, strength) · Correlation coefficient $r$ · Least-squares regression line $\hat{y} = a + bx$ · Slope and $y$-intercept interpretation in context · Residuals: observed $-$ predicted · Residual plots · Coefficient of determination $r^2$ · Log and power transformations for nonlinear data
standard track
5–7% of exam
Study unit ›
3.
Collecting Data
Sampling methods: SRS, stratified, cluster, systematic · Sources of bias: undercoverage, nonresponse, response, wording · Observational studies vs. experiments · Confounding and lurking variables · Experimental design: control, randomization, replication, blinding · Completely randomized designs · Randomized block designs · Matched pairs designs
standard track
12–15% of exam
Study unit ›
4.
Probability, Random Variables, and Probability Distributions
Basic probability rules: complement, addition, multiplication · Conditional probability: $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ · Independence of events · Two-way tables and tree diagrams · Discrete random variables: $E(X)$, $\text{Var}(X)$ · Combining independent RVs: means add, variances add · Binomial distribution (BINS conditions) · Geometric distribution · Normal distribution and $z$-scores
standard track
10–20% of exam
Study unit ›
5.
Sampling Distributions
Sampling distribution of $\bar{x}$: mean $= \mu$, SD $= \sigma/\sqrt{n}$ · Sampling distribution of $\hat{p}$: mean $= p$, SD $= \sqrt{p(1-p)/n}$ · Central Limit Theorem: shape for large $n$ · Conditions for normal approximation of $\bar{x}$ ($n \ge 30$ or population normal) · Large Counts condition for $\hat{p}$ ($np \ge 10$ and $n(1-p) \ge 10$) · 10% condition · Standard error vs. standard deviation
standard track
7–12% of exam
Study unit ›
6.
Inference for Categorical Data: Proportions
One-sample $z$-interval and $z$-test for proportion $p$ · Two-sample $z$-interval and $z$-test for $p_1 - p_2$ · Conditions: Random, 10%, Large Counts · Four-step procedure: State, Plan, Do, Conclude · Interpreting confidence levels and $p$-values in context · Type I error (false positive), Type II error (false negative) · Power: definition and factors that increase it · Width of confidence intervals
standard track
12–15% of exam
Study unit ›
7.
Inference for Quantitative Data: Means
One-sample $t$-interval and $t$-test for $\mu$ · Paired $t$-procedures for $\mu_d$ · Two-sample $t$-interval and $t$-test for $\mu_1 - \mu_2$ · Conditions: Random, 10%, Normality/CLT · Degrees of freedom for $t$-procedures · Assessing normality from plots (small $n$) vs. CLT (large $n$) · Interpreting results in context
standard track
10–18% of exam
Study unit ›
8.
Inference for Categorical Data: Chi-Square
Goodness-of-fit test: one sample, one variable vs. claimed distribution · Test for homogeneity: multiple populations, one variable · Test for independence: one population, two variables · Expected counts: $E = \frac{(\text{row total})(\text{col total})}{\text{table total}}$ · Conditions: Random, 10%, all expected counts $\ge 5$ · $\chi^2 = \sum \frac{(O-E)^2}{E}$ · Degrees of freedom
standard track
2–5% of exam
Study unit ›
9.
Inference for Quantitative Data: Slopes
$t$-test for slope: $H_0\colon \beta = 0$ vs. $H_a\colon \beta \ne 0$ · $t$-interval for slope $b$ · Conditions for regression inference: LINE + R (Linear, Independent, Normal, Equal variance, Random) · Reading computer regression output (coefficient, SE, $t$-statistic, $p$-value) · Standard error of the slope $SE_b$ · Degrees of freedom: $df = n - 2$
standard track
2–5% of exam
Study unit ›
FRQ Technique

The four-step inference procedure.

Every inference FRQ — confidence interval or significance test — follows the same four-step rubric. Missing any step costs rubric points even if your calculations are correct.

Step 1
State

Name the procedure. Define the parameter(s) in context. State hypotheses ($H_0$ and $H_a$) or describe the interval.

Step 2
Plan

Check all conditions: Random, 10% condition, and Large Counts (proportions) or Normality/CLT (means).

Step 3
Do

Calculate the test statistic or confidence interval. Show the formula, substitute values, and state the result with units.

Step 4
Conclude

Interpret in context. Compare $p$-value to $\alpha$. Use the correct language — never say "the null is true" or "we accept $H_0$."

Study Intelligence

High-frequency FRQ pain points.

#1 Most missed

Interpreting in context

Students compute the right number but write generic language. AP readers require the parameter to be named in context in every interpretation. "We are 95% confident the true proportion of [specific population] who [specific action] is between [a] and [b]."

#2 High cost

Conditions for inference

Forgetting to check all three conditions (Random, 10%, Large Counts) costs a rubric point per question. Never state "$n \ge 30$" as a blanket rule — you must assess the shape of the population or invoke CLT correctly.

#3

Paired vs. two-sample $t$

The data collection context — not the numbers — determines the correct test. Two measurements on the same subject = paired $t$. Two separate groups = two-sample $t$. Misidentifying the procedure typically scores a 1 on a 4-point question.

#4

Three chi-square tests

GOF (one sample, one variable vs. a claimed distribution) vs. homogeneity (multiple populations, same variable) vs. independence (one population, two variables). The expected count formula is the same for homogeneity and independence, but hypotheses and study design differ.

#5

Slope interpretation

Must include "predicted" and "on average": "For each additional [unit] in [X], the predicted [Y] increases by [b], on average." Residual = actual $-$ predicted (observed minus predicted), never the reverse.

#6

Combining random variables

Means always add: $\mu_{X \pm Y} = \mu_X \pm \mu_Y$. Variances add only when $X$ and $Y$ are independent: $\sigma^2_{X \pm Y} = \sigma^2_X + \sigma^2_Y$. Never add standard deviations directly.

Past Exam Questions

Released FRQ index.

AP Statistics has the largest archive of any AP STEM exam — approximately 228 FRQ problems spanning 1997–2025, including Form B variants. We index and deep-link only; we never reproduce question text or rehost College Board PDFs.

2025
AP Statistics FRQs (6 questions)
Q1: Data collection · Q2: Distributions · Q3: Probability · Q4: Inference · Q5: Combined · Q6: Investigative task
official CB release
Full scoring guidelines + sample responses
2024
AP Statistics FRQs (6 questions)
Q1: Data collection · Q2: Distributions · Q3: Probability · Q4: Inference · Q5: Combined · Q6: Investigative task
official CB release
Full scoring guidelines + sample responses
2023
AP Statistics FRQs (6 questions)
Q1: Data collection · Q2: Distributions · Q3: Probability · Q4: Inference · Q5: Combined · Q6: Investigative task
official CB release
Full scoring guidelines + sample responses
1997–2022
Historical Archive (~180 additional FRQs)
Full archive of released FRQs including Form B variants (2002B–2011B). Browse by topic on the official AP Central past-exam questions page.
AP Central archive
~228 total FRQs
Quick Reference

Essential formulas and conditions.

These appear on the formula sheet. What you must memorize: conditions, correct test selection, and contextual language.

Sampling Distributions

$$\mu_{\bar{x}} = \mu, \quad \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$ $$\mu_{\hat{p}} = p, \quad \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$$

Standardized Test Statistics

$$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$$ $$t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}, \quad df = n-1$$

Chi-Square Statistic

$$\chi^2 = \sum \frac{(O - E)^2}{E}$$ $$E = \frac{(\text{row total})(\text{col total})}{\text{table total}}$$

Our worked solutions and practice questions are original instructional content created by Tian2 AP. They are aligned to the concepts and skills described in College Board’s Course and Exam Description and are not reproductions of, or affiliated with, College Board’s official materials.