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AP Statistics
Practice Exam

All major units  ·  Real AP difficulty  ·  Detailed explanations

20
Questions
8
Units
45
Minutes
📚 Concept Review & Key Formulas Hide
Unit 1 · Exploring One-Variable Data
Key Concept
Describing Distributions (SOCS)
Always report: Shape, Outliers, Center, Spread. In right-skewed distributions, mean > median because the mean is pulled toward the tail.
IQR = Q3 − Q1 Outlier if: x < Q1 − 1.5·IQR or x > Q3 + 1.5·IQR Variance: s² = Σ(xᵢ − x̄)² / (n−1)
Example
Q1=18, Q3=32. Is x=55 an outlier?
IQR=14. Upper fence = 32 + 1.5(14) = 53. Since 55 > 53, YES — 55 is an outlier.
Unit 2 · Exploring Two-Variable Data
Key Concept
Regression & Correlation
r² = % of variation in y explained by x. The slope b = r(Sᵧ/Sₓ). Residual = Observed − Predicted (positive means above the line). Correlation ≠ causation.
ŷ = a + bx where b = r·(Sᵧ/Sₓ), a = ȳ − b·x̄ Residual = y − ŷ
Example
r = 0.85. What % of variation in y is explained by x?
r² = 0.7225 → 72.25% explained by the linear relationship.
Unit 3 · Collecting Data
Key Concept
Sampling Methods & Experiments
Stratified: SRS within subgroups. Cluster: randomly select whole groups. Only randomized experiments can establish causation. Confounding: a variable related to both explanatory & response variables.
Principles of Experiments: Control · Randomization · Replication · Blinding
Unit 4 · Probability, Random Variables & Distributions
Key Concept
Probability & Binomial Distribution
P(A|B) = P(A∩B)/P(B). Binomial conditions: Binary, Independent, fixed Number n, same P. Geometric: # trials until first success.
P(X=k) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ μ(Binomial) = np, σ = √(np(1−p)) E(X) = Σ x·P(X=x) Geometric: μ = 1/p
Example
n=12, p=0.5 (fair coin). Find mean and SD of heads.
μ = 12·0.5 = 6. σ = √(12·0.5·0.5) = √3 ≈ 1.73.
Unit 5 · Sampling Distributions
Key Concept
Central Limit Theorem
For n ≥ 30, the sampling distribution of x̄ is approximately Normal regardless of population shape. For p̂: Normal when np ≥ 10 and n(1−p) ≥ 10.
μ(x̄) = μ, σ(x̄) = σ/√n (Standard Error) μ(p̂) = p, σ(p̂) = √(p(1−p)/n)
Unit 6 · Inference for Proportions
Key Concept
z-Tests & Confidence Intervals for p
Correct interpretation: "We are C% confident the interval captures the true parameter." The parameter p is fixed; the interval is random. Conditions: Random, Normal (np≥10, n(1−p)≥10), Independent (10% rule).
CI: p̂ ± z*·√(p̂(1−p̂)/n) z-test: z = (p̂ − p₀) / √(p₀(1−p₀)/n)
Unit 7 · Inference for Means
Key Concept
t-Tests & t-Intervals
Use t-distribution when σ is unknown. df = n−1 for one-sample. Matched pairs: compute differences first, then apply one-sample t-test. Type I error (α): reject true H₀. Type II error (β): fail to reject false H₀.
CI: x̄ ± t*·(s/√n), df = n−1 t-test: t = (x̄ − μ₀) / (s/√n) Paired: t = d̄ / (sᴅ/√n), df = n−1
Unit 8 · Chi-Square Tests
Key Concept
Goodness-of-Fit, Independence & Homogeneity
All expected counts must be ≥ 5. Chi-square is always right-tailed. GOF: compares one variable to a claimed distribution. Independence/Homogeneity: two-way tables.
χ² = Σ (O − E)² / E Expected = (Row total × Col total) / Grand total df (GOF) = categories − 1 df (two-way table) = (rows−1)(cols−1)
Example
3×4 table. Find degrees of freedom.
df = (3−1)(4−1) = (2)(3) = 6.
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