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AP Statistics FRQ 2025

Complete Step-by-Step Worked Solutions

A cleaner, more engaging walkthrough for students: smoother layout, easier navigation, playful visuals, and expandable solutions that feel interactive instead of overwhelming.

Student-friendly explanations All 6 FRQs covered Better accordion UX Responsive & polished
6 Free-response questions
2025 Official exam paper
Step-by-step Exam-style reasoning

About This AP Statistics 2025 FRQ Paper

Overview

This page organizes the 2025 AP Statistics free-response paper into a smoother learning experience. Students can move question by question, open the full walkthrough only when needed, and focus on the most important reasoning patterns.

What students learn Compare distributions, explain sampling bias, work with binomial models, and interpret inference.
Why this layout works better Shorter visual chunks, clear labels, expandable sections, and less text overload at first glance.

Original 2025 AP Statistics FRQ Paper

Reference

Use the official paper alongside these solutions so students can compare the original boxplots, wording, and prompt structure with the worked explanations below.

Open Official PDF in New Tab
If the embedded preview does not load on a device, the direct “Open Official PDF” button will still work.

Question-by-Question Worked Solutions

Step-by-step
Comparing distributions Boxplots No calculator needed

Question summary

The problem compares side-by-side boxplots for 100 cars from Country A and 100 cars from Country B. Students must compare center, spread, shape, and outliers, then reason about mean vs median and about the combined data set.

Quick recap

A boxplot helps you discuss five key ideas: minimum, Q1, median, Q3, and maximum. On AP Statistics, “compare” means talk about both groups together, not separately.

Part A – Compare the two distributions

Country B has the higher median gas mileage, so a typical car from Country B gets better mileage than a typical car from Country A. Country B also appears more spread out overall, with a larger range and a slightly larger IQR.

Country A is right-skewed and has a high outlier, while Country B looks roughly symmetric with no clear outliers.

Common error

Students often describe only one graph at a time. Use language like “higher than,” “more variable than,” and “more skewed than.”

Part B – Mean vs median for Country A

Because Country A is right-skewed and has a high outlier, the mean should be greater than the median. The right tail pulls the mean upward.

Part C – Combined data

For the combined range, take the largest value from all 200 cars and subtract the smallest value from all 200 cars. For the combined median, a value around 24 mpg is reasonable because it balances the ordered data from both groups.

Sampling methods Bias Design

Question summary

A cabbage field is split into a 5×5 grid, and the farmer believes damage is worse closer to the river. Students must judge sample quality and describe a better random method.

Core idea

A strong sample should represent the whole field and avoid overusing one convenient area.

Part A – Method I

Sampling only one region near the house is not appropriate. It is a convenience sample and can be biased because it may ignore the regions nearer the river where damage could be greater.

Part B – Method II

If row E is closest to the river and the farmer’s belief is correct, using only row E would likely overestimate the overall proportion of damaged plants.

Part C – Method III

A strong method is to randomly select one region from each row. That guarantees representation across the field while still using randomness.

  1. Label regions 1–5 within each row.
  2. Use a random number generator to choose one region in row A.
  3. Repeat independently for rows B, C, D, and E.
  4. Inspect every cabbage plant in the five selected regions.
Probability Binomial distribution Calculator helpful

Question summary

A playlist has 1,000 songs, including 100 rock songs. Songs are selected with replacement. Students work with simple probabilities, define a binomial random variable, and judge whether an observed result is unusual.

Binomial checklist

Fixed number of trials, independent trials, two outcomes, constant probability of success.

Part A – Simple probabilities

The probability one randomly selected song is rock is:

P(rock) = 100 / 1000 = 0.10

The probability that two selected songs are both rock is:

0.10 × 0.10 = 0.01

Part B – Random variable and expected value

Let X be the number of rock songs among 20 randomly selected songs. Then:

X ~ Binomial(n = 20, p = 0.10)

The expected value is:

E(X) = np = 20(0.10) = 2

Part C – At least 4 rock songs

Use the complement:

P(X ≥ 4) = 1 - P(X ≤ 3) ≈ 0.133

Since 0.133 is not especially small, getting 4 rock songs does not give strong evidence that the playlist process is not random.

Calculator tip

This is a good place for a binomial cumulative function on a graphing calculator.

1-Prop z test Inference Alpha = 0.05

Question summary

A national proportion is 0.22. Karen samples 130 students and finds 38 use a homework-help app weekly. She believes her school’s proportion is greater.

Step 1 – Hypotheses

H₀: p = 0.22
Hₐ: p > 0.22

Step 2 – Conditions

  • Random sample given
  • 130 is less than 10% of the school population
  • Expected successes and failures under H₀ are both at least 10

Step 3 – Test statistic

p̂ = 38 / 130 ≈ 0.2923 z = (0.2923 - 0.22) / √[(0.22)(0.78)/130] ≈ 1.99

Step 4 – p-value and conclusion

The one-sided p-value is about 0.023. Since 0.023 < 0.05, reject H₀.

There is convincing evidence that the proportion of students at Karen’s school who use the app weekly is greater than 0.22.

Common error

For the z test of a proportion, use the null proportion in the standard error, not the sample proportion.

Discrete distribution t test Confidence interval link

Question summary

Students work with a bedroom-count distribution, then connect a two-sided hypothesis test to a 97% confidence interval.

Part A – Probability and mean

The probability of fewer than 3 bedrooms is:

P(1 or 2 bedrooms) = 0.12 + 0.22 = 0.34

The mean number of bedrooms is the weighted average:

μ = 1(0.12) + 2(0.22) + 3(0.28) + 4(0.22) + 5(0.14) + 6(0.02) = 3.10

Part B – Hypotheses

H₀: μ = 2.9
Hₐ: μ ≠ 2.9

A Type I error here means concluding the 2024 mean number of bedrooms is different from 2.9 when it is actually still 2.9.

Part C – Confidence interval link

The 97% confidence interval is (3.01, 3.19). Since 2.9 is not in that interval, reject H₀ at α = 0.03.

There is evidence that the 2024 mean is different from 2.9, and the interval suggests it is higher.

Two-sample t test Cohen’s d Practical importance

Question summary

50 children take the reading task at 9 a.m. and 50 take it at 3 p.m. The study compares two independent groups.

Part A – Hypothesis test conclusion

The p-value is 0.002, which is less than 0.05, so reject H₀. There is strong evidence that mean reading scores differ between the two times.

Because the 3 p.m. mean is higher, the data suggest better performance at 3 p.m.

Part B – Why two-sample t and not paired t?

Each child was assigned to only one time slot, so the groups are independent. A paired t test would only make sense if the same children were measured twice.

Part C – Cohen’s d

sₚ = √[(4.12² + 4.43²)/2] ≈ 4.28 d = |15.2 - 17.9| / 4.28 ≈ 0.63

A Cohen’s d of about 0.63 is moderately meaningful in real life.

Part D – If the standard deviations were larger

If variability increases while the means stay the same, the pooled standard deviation increases, so Cohen’s d becomes smaller. That makes the practical importance weaker.

Big AP reminder

Statistical significance and practical importance are not the same thing. Always check both.

Key Concepts Students Reinforce

Concept recap
  • How to compare distributions using shape, center, spread, and outliers
  • How poor sampling methods create bias
  • How and when to use a binomial model
  • How to interpret one-sample and two-sample inference
  • How to separate statistical significance from practical significance

How to Revise With This Page

Study strategy

1. Attempt first, then expand

Have students attempt each FRQ before opening the solution panel. That turns the page into active practice instead of passive reading.

2. Focus on command words

Ask students to circle words like compare, justify, determine, and interpret. Then show how the solution structure matches the command.

3. Build an error log

Each time a student makes a repeated mistake, add it to a personal “watch out” list and review it before the next practice set.

4. Practice the conclusion sentence

Students should be able to say: because the p-value is less than alpha, reject H₀; there is evidence that...

5. Use the calculator deliberately

Probability and inference become much faster when students actually know which function to use and why.

FAQ

Student help

Not for every part. Concept questions can be done by reasoning alone, but binomial probabilities and inference are faster and safer with a graphing calculator.

Usually a sensible rounded answer is fine if the method is correct and the work is consistent.

Yes. If the reasoning is statistically valid and clearly explained, alternative correct methods can still earn credit.

Practice writing conclusions in context, not just doing calculations. Most lost marks come from incomplete explanation.