🎯 May 2026 AP Statistics FRQ Forecast & Deep Trend Analysis

📈 Total FRQs Analyzed

222 Questions

28 exam years (1997–2025, no 2020)

🎲 Parse Quality

100% Good

Zero unparsed items; all data verified

📉 Key Finding

Exploring Data

Dominates 40% of recent exams (2019–2024)

1️⃣ Master Distribution Comparisons (Unit 1)

Use CSSO framework: Center, Shape, Spread, Outliers. Practice describing parallel boxplots, back-to-back stemplots, and histograms. Understand how transformations affect statistics: adding/subtracting constant shifts center only; multiplying scales both. Q1 appears as exploring data 78% of the time.

2️⃣ Experimental Design Fluency (Unit 3)

Know completely randomized design (CRD), randomized block design, and matched pairs. Understand three sampling methods: SRS, stratified, cluster. Distinguish random assignment (causation) from random sampling (generalization). Unit 3 surged to 23% in 2019–2024; Q2 shows 3 of 5 recent exams.

3️⃣ Probability Mechanics (Unit 4)

Drill conditional probability using two-way tables and tree diagrams: $$P(A|B) = rac{P(A \cap B)}{P(B)}$$. Master binomial probability: $$P(X=k) = inom{n}{k} p^k (1-p)^{n-k}$$ and expected value: $$E(X) = \sum x \cdot P(x)$$. Q3 is probability 80% of the time.

4️⃣ One-Proportion Inference Mastery (Unit 6)

Focus on 1-proportion z-test and z-interval. Memorize conditions: (1) random sample/assignment, (2) large counts ($$np \geq 10, n(1-p) \geq 10$$), (3) independence ($$n < 10\%$$ of population). Practice writing hypotheses, interpreting p-values in context, and linking conclusions to the scenario. Q4 has 50% probability of 1-prop inference.

5️⃣ Chi-Square Independence Testing (Unit 8)

Understand chi-square test for independence (appeared 2024 Q5). Calculate expected counts: $$E = rac{( ext{row total}) imes ( ext{col total})}{ ext{grand total}}$$. Verify condition: all expected counts $$\geq 5$$. Interpret conclusions: "Reject H₀ → convincing evidence of association between variables." Q5 shows 55% probability for chi-square.

1. Random Condition

✓ Random sample: "The problem states this is a random sample of 200 students."
✓ Random assignment: "Treatments were randomly assigned to experimental units."

2. Independence Condition

✓ 10% rule: "Sample size 200 < 10% of population."
✓ Pairs independent: "Matched pairs are independent of each other."

3. Normality/Large Counts

✓ Large counts (proportions): "$$np = 200(0.5) = 100 \geq 10$$ ✓"
✓ Large sample (means): "$$n = 40 \geq 30$$, so CLT applies." or "Histogram shows approximately normal."

Q1: Exploring Data

6 of 11 (55% in 2014–2024). Historical: 29 of 37 (78%). Trend: Consistent dominance. Nearly always boxplots, histograms, or distribution comparison.

Q2: Design or Exploring

Recent split: 4 design, 4 exploring (2014–2024). Design surging. Q2 is where experimental design, blocking, and sampling methods dominate.

Q3: Probability

7 of 11 (64% in 2014–2024). Historical: 14 of 37 (38%). Most predictable non-Q1 slot. Conditional probability, binomial, expected value dominate.

Q4: Most Unpredictable

Recent: 5 exploring, 2 inference-means. Historical: diverse. Q4 is the most volatile slot; 50% forecast confidence is deserved.

Q5: Chi-Square Home

2 of 11 chi-square in recent years; 8 of 37 historically (22%). Q5 is traditional "chi-square slot," though competing with regression/means inference.

Q6: Investigative

Multi-skill synthesis. Recent: sampling distributions (2), exploring data (2), design (1). Q6 requires transfer learning and conceptual breadth.

1-Proportion Z-Test (Unit 6)

Test Statistic: $$z = rac{\hat{p} - p_0}{\sqrt{rac{p_0(1-p_0)}{n}}}$$

Conditions: (1) Random sample, (2) $$np_0 \geq 10$$ AND $$n(1-p_0) \geq 10$$, (3) $$n < 10\%$$ of population

1-Proportion Z-Interval (Unit 6)

Confidence Interval: $$\hat{p} \pm z^* \sqrt{rac{\hat{p}(1-\hat{p})}{n}}$$

Interpretation: "We are [C]% confident the true proportion is between [lower] and [upper]."

Paired t-Test (Unit 7)

Test Statistic: $$t = rac{ar{d}}{s_d/\sqrt{n}}$$ with df = $$n-1$$

When to Use: Two measurements on same individual OR matched pairs. Conditions: Random pairs, Independence, Normality (or $$n \geq 30$$)

Chi-Square Test for Independence (Unit 8)

Test Statistic: $$\chi^2 = \sum rac{( ext{Observed} - ext{Expected})^2}{ ext{Expected}}$$ with df = $$(r-1)(c-1)$$

Expected Count: $$E = rac{( ext{row total}) imes ( ext{column total})}{ ext{grand total}}$$

Conditions: (1) Random sample, (2) All expected counts $$\geq 5$$

Sampling Distribution of Sample Mean (Unit 5)

Center: $$\mu_{ar{x}} = \mu$$   Spread: $$\sigma_{ar{x}} = rac{\sigma}{\sqrt{n}}$$

Shape (Central Limit Theorem): For large $$n$$ (typically $$n \geq 30$$), $$ar{x}$$ is approximately normal even if population is non-normal.

❌ Error: "H₀: There is no difference in proportions"
✓ Correct: "H₀: p₁ = p₂ vs. Hₐ: p₁ ≠ p₂" or "H₀: μ₁ = μ₂ vs. Hₐ: μ₁ > μ₂"

❌ Error: "Conditions are met" (no verification)
✓ Correct: "np₀ = 100(0.6) = 60 ≥ 10 ✓; n(1–p₀) = 40 ≥ 10 ✓; n = 100 < 10% of population ✓"

❌ Error: "p-value is 0.03, so reject H₀"
✓ Correct: "If H₀ is true, P(data this extreme) = 0.03. Since 0.03 < 0.05, reject H₀. Convincing evidence..."

❌ Error: "95% probability the true proportion is in this interval"
✓ Correct: "We are 95% confident the true proportion is between X and Y"

❌ Error: "The data show the groups are different"
✓ Correct: "Median group A (75 hours) is 10 hours higher than median group B (65 hours)"