AP Statistics — Official Practice Quiz

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Unit 1

Exploring Data — Distributions & Summary Statistics

Shape: Symmetric, skewed left (mean < median), skewed right (mean > median)
Center: Mean (affected by outliers), Median (resistant)
Spread: Range, IQR = Q3 − Q1, Standard Deviation s
Outlier rule: values beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR
z-score: number of standard deviations from mean

Formulas to Memorize

z = (x − μ) / σ
IQR = Q3 − Q1
s = √[ Σ(xᵢ − x̄)² / (n−1) ]

⚡ Memory Tip

Skewed right → tail goes right → mean is pulled right → mean > median. Think: the tail chases the mean!

Example

Data: 2, 4, 4, 6, 8, 10, 50 — Which is larger, mean or median?
Mean = 84/7 ≈ 12, Median = 6. Mean > Median → right-skewed (outlier 50 pulls mean up).

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Unit 2

Sampling Methods & Experimental Design

SRS (Simple Random Sample): every individual has equal chance
Stratified: divide into homogeneous groups, SRS from each
Cluster: divide into groups, randomly select entire groups
Systematic: every kth individual; convenience = biased
Experiment: control, randomize, replicate. Only experiments show causation.
Confounding: lurking variable that affects response variable
Blocking: group experimental units by a known source of variability

⚡ Key Distinction

Observational study → association only. Experiment with random assignment → causation. Random sampling → generalize to population. Random assignment → cause-and-effect.

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Unit 3

Probability Rules & Conditional Probability

0 ≤ P(A) ≤ 1; P(S) = 1; P(Aᶜ) = 1 − P(A)
Addition rule: P(A∪B) = P(A) + P(B) − P(A∩B)
Mutually exclusive: P(A∩B) = 0
Independent: P(A∩B) = P(A)·P(B)
Conditional: P(A|B) = P(A∩B) / P(B)

Core Formulas

P(A|B) = P(A∩B) / P(B)
P(A∩B) = P(A)·P(B|A)
Independent ⟺ P(A|B) = P(A)

⚡ Common Trap

Mutually exclusive ≠ independent! If A and B are mutually exclusive (can't both happen), knowing one occurred makes the other impossible → they ARE dependent.

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Unit 4

Random Variables — Binomial & Geometric

E(X) = μ = Σ xᵢ·P(xᵢ) for discrete RV
Var(X) = Σ (xᵢ − μ)²·P(xᵢ)
Binomial: fixed n, binary outcome, constant p, independent trials (BINS)
Geometric: count trials until first success

Binomial Formulas

P(X=k) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ
μ_X = np
σ_X = √(np(1−p))
Geometric: E(X) = 1/p

⚡ BINS Checklist for Binomial

B — Binary outcome I — Independent trials N — Fixed number of trials S — Same probability p

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Unit 5

Sampling Distributions & Central Limit Theorem

Sampling distribution of x̄: μ_x̄ = μ, σ_x̄ = σ/√n
CLT: As n increases, distribution of x̄ approaches Normal regardless of population shape
Rule of thumb: n ≥ 30 for CLT to apply (or n < 30 if population is Normal)
Sampling distribution of p̂: μ_p̂ = p, σ_p̂ = √(p(1−p)/n)
Normal condition for p̂: np ≥ 10 AND n(1−p) ≥ 10

Standard Error Formulas

SE(x̄) = σ/√n or s/√n
SE(p̂) = √(p(1−p)/n)
z = (x̄ − μ) / (σ/√n)

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Units 6–7

Confidence Intervals & Significance Tests

CI: statistic ± (critical value) × (standard error)
Wider CI: lower confidence level ↓, larger n ↑, smaller σ ↓
Interpret CI: "We are 95% confident the true parameter is between ___ and ___."
H₀: null hypothesis (no effect); Hₐ: alternative (effect exists)
p-value: probability of seeing result as extreme as observed, assuming H₀ true
If p < α (usually 0.05) → reject H₀
Type I error: reject true H₀ (α = P(Type I)). Type II error: fail to reject false H₀.
Power = 1 − P(Type II error). Power ↑ with larger n, larger effect size, larger α.

One-Sample z-interval for proportion

p̂ ± z* · √(p̂(1−p̂)/n)
t* used when σ unknown; df = n−1
t = (x̄ − μ₀) / (s/√n)

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Units 8–9

Chi-Square Tests & Linear Regression

χ² GOF test: Is observed distribution consistent with expected?
χ² test of independence: Are two categorical variables associated?
Expected cell count ≥ 5 for all cells; df = (rows−1)(cols−1)
LSRL: ŷ = b₀ + b₁x; b₁ = r·(sᵧ/sₓ); b₀ = ȳ − b₁x̄
r² = fraction of variability in y explained by linear regression on x
Residual = observed − predicted = y − ŷ
No pattern in residual plot → linear model is appropriate

Regression & Chi-Square

ŷ = b₀ + b₁x
b₁ = r·(sᵧ/sₓ) ; b₀ = ȳ − b₁x̄
χ² = Σ (O−E)² / E

⚡ r vs r²

r = correlation (direction + strength, −1 to 1). r² = coefficient of determination (0 to 1, always ≥ 0). r² tells you % of variation explained.

AP Statistics
Practice Quiz

Key Concepts & Formulas

AP StatisticsPractice Quiz

Key Concepts & Formulas

AP Statistics
Practice Quiz