AP STATISTICS | 2026–27 COURSE | WORKED SOLUTIONS
AP STATISTICS
2026–27 Course Examination
1,000 Questions
Fully Worked Calculations • Answer Keys • Explanations
• 1
, AP STATISTICS | 2026–27 COURSE | WORKED SOLUTIONS
UNIT 1 | EXPLORING ONE-VARIABLE DATA AND COLLECTING DATA
1. A data set at a school district includes a single very large new observation. Which
summary is most likely to change markedly?
A. The mean
B. The 25th percentile of a large existing sample
C. The number of categories
D. The median of a large existing sample
Correct answer: A. The mean
Explanation: The mean uses every magnitude and is sensitive to extreme values. Resistant
summaries such as a median usually change less.
2. Scores from a community college have standard deviation 6. A new score is calculated
as 4 times the old score plus 10. What is the new standard deviation?
A. 34.0
B. 6.0
C. 16.0
D. 24.0
Correct answer: D. 24.0
𝑠_𝑦 = 𝑎𝑏𝑠(𝑏)𝑠_𝑥
𝑠_𝑦 = 4 × 6
𝑠_𝑦 = 24.0
Explanation: Adding 10 shifts all scores but does not change their spread. Multiplying each
score by 4 multiplies the standard deviation by |4|, so the new SD is 24.
3. A statistician at a museum adds the same fixed constant to every observation. Which
result remains unchanged?
A. The standard deviation
B. The minimum
C. The mean
D. The median
Correct answer: A. The standard deviation
Explanation: Shifting every value by a constant changes location measures by that constant but
leaves all pairwise differences and the SD unchanged.
• 2
, AP STATISTICS | 2026–27 COURSE | WORKED SOLUTIONS
4. An administrator at a water-quality laboratory finds that people who participate in a
voluntary wellness program have lower average stress than nonparticipants. What is the
strongest warranted conclusion?
A. The lack of random assignment is irrelevant.
B. The lower average proves every participant benefited.
C. An association is observed, but self-selection may confound a causal conclusion.
D. The program must have caused lower stress.
Correct answer: C. An association is observed, but self-selection may confound a causal
conclusion.
Explanation: Because people selected whether to participate, groups may differ in motivation,
baseline health, or other factors. An observational association does not establish cause and
effect.
5. A dotplot of 100 survey observations from a public health team shows 25
observations above a stated threshold. What fraction of all observations lies above that
threshold?
A. 0.333
B. 0.750
C. 0.250
D. 0.300
Correct answer: C. 0.250
𝑘
𝑓 =
𝑛
25
𝑓 =
100
𝑓 = 0.250
Explanation: Exactly 25 out of 100 are above the threshold, so the relative frequency is
25/100=0.250.
• 3
, AP STATISTICS | 2026–27 COURSE | WORKED SOLUTIONS
6. A sample of 15 readings at a public library has mean 71. One reading of 67 was
entered incorrectly and should be 112. What is the corrected mean?
A. 116.00
B. 68.00
C. 74.00
D. 74.21
Correct answer: C. 74.00
𝑛𝑀₁ − 𝑤 + 𝑐
𝑀₂ =
𝑛
15 × 71 − 67 + 112
𝑀₂ =
15
𝑀₂ = 74.00
Explanation: The original total is 15×71. Replace 67 with 112, increasing the total by 45;
divide by the same n=15. The corrected mean is 74.00.
7. Five observations recorded by a regional hospital are 52, 41, 48, 27, 33. What is their
arithmetic mean?
A. 50.25
B. 33.50
C. 40.20
D. 41.00
Correct answer: C. 40.20
𝛴 𝑥ᵢ
𝑥 =
𝑛
52 + 41 + 48 + 27 + 33
𝑥 =
5
𝑥 = 40.20
Explanation: The mean equals the sum divided by the number of observations:
(52+41+48+27+33)/5=40.20. Unlike the median, every observation contributes to the mean.
• 4
AP STATISTICS
2026–27 Course Examination
1,000 Questions
Fully Worked Calculations • Answer Keys • Explanations
• 1
, AP STATISTICS | 2026–27 COURSE | WORKED SOLUTIONS
UNIT 1 | EXPLORING ONE-VARIABLE DATA AND COLLECTING DATA
1. A data set at a school district includes a single very large new observation. Which
summary is most likely to change markedly?
A. The mean
B. The 25th percentile of a large existing sample
C. The number of categories
D. The median of a large existing sample
Correct answer: A. The mean
Explanation: The mean uses every magnitude and is sensitive to extreme values. Resistant
summaries such as a median usually change less.
2. Scores from a community college have standard deviation 6. A new score is calculated
as 4 times the old score plus 10. What is the new standard deviation?
A. 34.0
B. 6.0
C. 16.0
D. 24.0
Correct answer: D. 24.0
𝑠_𝑦 = 𝑎𝑏𝑠(𝑏)𝑠_𝑥
𝑠_𝑦 = 4 × 6
𝑠_𝑦 = 24.0
Explanation: Adding 10 shifts all scores but does not change their spread. Multiplying each
score by 4 multiplies the standard deviation by |4|, so the new SD is 24.
3. A statistician at a museum adds the same fixed constant to every observation. Which
result remains unchanged?
A. The standard deviation
B. The minimum
C. The mean
D. The median
Correct answer: A. The standard deviation
Explanation: Shifting every value by a constant changes location measures by that constant but
leaves all pairwise differences and the SD unchanged.
• 2
, AP STATISTICS | 2026–27 COURSE | WORKED SOLUTIONS
4. An administrator at a water-quality laboratory finds that people who participate in a
voluntary wellness program have lower average stress than nonparticipants. What is the
strongest warranted conclusion?
A. The lack of random assignment is irrelevant.
B. The lower average proves every participant benefited.
C. An association is observed, but self-selection may confound a causal conclusion.
D. The program must have caused lower stress.
Correct answer: C. An association is observed, but self-selection may confound a causal
conclusion.
Explanation: Because people selected whether to participate, groups may differ in motivation,
baseline health, or other factors. An observational association does not establish cause and
effect.
5. A dotplot of 100 survey observations from a public health team shows 25
observations above a stated threshold. What fraction of all observations lies above that
threshold?
A. 0.333
B. 0.750
C. 0.250
D. 0.300
Correct answer: C. 0.250
𝑘
𝑓 =
𝑛
25
𝑓 =
100
𝑓 = 0.250
Explanation: Exactly 25 out of 100 are above the threshold, so the relative frequency is
25/100=0.250.
• 3
, AP STATISTICS | 2026–27 COURSE | WORKED SOLUTIONS
6. A sample of 15 readings at a public library has mean 71. One reading of 67 was
entered incorrectly and should be 112. What is the corrected mean?
A. 116.00
B. 68.00
C. 74.00
D. 74.21
Correct answer: C. 74.00
𝑛𝑀₁ − 𝑤 + 𝑐
𝑀₂ =
𝑛
15 × 71 − 67 + 112
𝑀₂ =
15
𝑀₂ = 74.00
Explanation: The original total is 15×71. Replace 67 with 112, increasing the total by 45;
divide by the same n=15. The corrected mean is 74.00.
7. Five observations recorded by a regional hospital are 52, 41, 48, 27, 33. What is their
arithmetic mean?
A. 50.25
B. 33.50
C. 40.20
D. 41.00
Correct answer: C. 40.20
𝛴 𝑥ᵢ
𝑥 =
𝑛
52 + 41 + 48 + 27 + 33
𝑥 =
5
𝑥 = 40.20
Explanation: The mean equals the sum divided by the number of observations:
(52+41+48+27+33)/5=40.20. Unlike the median, every observation contributes to the mean.
• 4
