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Academic Support AP Statistics Unit 1: Exploring One-Variable Data and Collecting Data

Exploring One-Variable Data: Shape, Center, Spread, and Outliers

36 visible MCQs, 14 FRQ sets, formulas, worked answers, and direct links to the complete AP Statistics practice system.

Published July 18, 2026Updated August 7, 2026By Engr. Muhammad Yar Saqib40 min read
Statistics guide Ethical learning support SPSS/R/Python/Excel friendly
AP Statistics Practice

Exploring One-Variable Data: Shape, Center, Spread, and Outliers

Exploring One-Variable Data: Shape, Center, Spread, and Outliers practice bank: Solve the visible multiple-choice and free-response questions, then compare every step with the worked answers.

MCQs36
FRQ sets14
AnswersVisible
Topic links73 pages

Exploring One-Variable Data: Shape, Center, Spread, and Outliers: formulas and targets

Meanx̄ = Σxn
Sample SDs = √Σ(x−x̄)2(n−1)
IQRQ3−Q1

Exploring One-Variable Data multiple-choice practice

Question 1. Exploring One-Variable Data

The municipal emergency dispatch center in Sunbelt district during a baseline measurement week records nine response time values: [15, 19, 29, 30, 52, 61, 62, 69, 79]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 416, median 52, IQR 20.75.
  2. B. Mean 46.222, median 52, IQR 41.5.
  3. C. Mean 52, median 46.222, IQR 64.
  4. D. Mean 46.222, median 52, IQR 89.5.

Answer: B

The mean is 4169=46.222 and the median is the fifth ordered value, 52. Q1=24, Q3=65.5, so IQR=41.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 46.222, median 52, IQR 41.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 46.222, median 52, IQR 41.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 46.222, median 52, IQR 41.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 2. Exploring One-Variable Data

The food safety laboratory in Pacific Northwest during a monthly quality review records nine sample concentration values: [25, 35, 41, 52, 55, 60, 64, 79, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 54.556, median 55, IQR 109.5.
  2. B. Mean 55, median 54.556, IQR 55.
  3. C. Mean 54.556, median 55, IQR 33.5.
  4. D. Mean 491, median 55, IQR 16.75.

Answer: C

The mean is 4919=54.556 and the median is the fifth ordered value, 55. Q1=38, Q3=71.5, so IQR=33.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 54.556, median 55, IQR 33.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 54.556, median 55, IQR 33.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 54.556, median 55, IQR 33.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 3. Exploring One-Variable Data

The public high school in Cedar Grove during a weekday operations study records nine algebra benchmark completion values: [12, 18, 25, 38, 51, 57, 69, 75, 84]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 51, median 47.667, IQR 72.
  2. B. Mean 47.667, median 51, IQR 93.5.
  3. C. Mean 47.667, median 51, IQR 50.5.
  4. D. Mean 429, median 51, IQR 25.25.

Answer: C

The mean is 4299=47.667 and the median is the fifth ordered value, 51. Q1=21.5, Q3=72, so IQR=50.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 47.667, median 51, IQR 50.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 47.667, median 51, IQR 50.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 47.667, median 51, IQR 50.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 4. Exploring One-Variable Data

The farm cooperative in South Harbor during a yearly program evaluation records nine crop yield values: [18, 25, 43, 52, 57, 63, 65, 75, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 53.111, median 57, IQR 104.0.
  2. B. Mean 478, median 57, IQR 18.
  3. C. Mean 57, median 53.111, IQR 62.
  4. D. Mean 53.111, median 57, IQR 36.

Answer: D

The mean is 4789=53.111 and the median is the fifth ordered value, 57. Q1=34, Q3=70, so IQR=36. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 57, IQR 36. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 57, IQR 36. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 57, IQR 36. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 5. Exploring One-Variable Data

The solar installer in Westview during a monthly quality review records nine daily energy output values: [14, 28, 45, 48, 58, 59, 66, 70, 73]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 51.222, median 58, IQR 31.5.
  2. B. Mean 58, median 51.222, IQR 59.
  3. C. Mean 461, median 58, IQR 15.75.
  4. D. Mean 51.222, median 58, IQR 104.5.

Answer: A

The mean is 4619=51.222 and the median is the fifth ordered value, 58. Q1=36.5, Q3=68, so IQR=31.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 51.222, median 58, IQR 31.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 51.222, median 58, IQR 31.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 51.222, median 58, IQR 31.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 6. Exploring One-Variable Data

The community bank in North Valley during a pre-exam training cycle records nine mobile-deposit adoption values: [16, 35, 50, 52, 62, 70, 73, 74, 77]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 509, median 62, IQR 15.5.
  2. B. Mean 62, median 56.556, IQR 61.
  3. C. Mean 56.556, median 62, IQR 116.0.
  4. D. Mean 56.556, median 62, IQR 31.

Answer: D

The mean is 5099=56.556 and the median is the fifth ordered value, 62. Q1=42.5, Q3=73.5, so IQR=31. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 56.556, median 62, IQR 31. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 56.556, median 62, IQR 31. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 56.556, median 62, IQR 31. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 7. Exploring One-Variable Data

The university advising center in Sunbelt district during a spring 2027 pilot records nine appointment wait time values: [29, 31, 33, 56, 57, 62, 77, 78, 79]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 57, median 55.778, IQR 50.
  2. B. Mean 55.778, median 57, IQR 109.5.
  3. C. Mean 502, median 57, IQR 22.75.
  4. D. Mean 55.778, median 57, IQR 45.5.

Answer: D

The mean is 5029=55.778 and the median is the fifth ordered value, 57. Q1=32, Q3=77.5, so IQR=45.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 55.778, median 57, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 55.778, median 57, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 55.778, median 57, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 8. Exploring One-Variable Data

The regional airport authority in Capital Region during a semester-long cohort study records nine security wait time values: [13, 15, 18, 30, 33, 37, 50, 51, 55]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 302, median 33, IQR 17.
  2. B. Mean 33.556, median 33, IQR 34.
  3. C. Mean 33, median 33.556, IQR 42.
  4. D. Mean 33.556, median 33, IQR 67.

Answer: B

The mean is 3029=33.556 and the median is the fifth ordered value, 33. Q1=16.5, Q3=50.5, so IQR=34. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 33.556, median 33, IQR 34. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 33.556, median 33, IQR 34. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 33.556, median 33, IQR 34. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 9. Exploring One-Variable Data

The municipal water office in Great Lakes during a six-week field trial records nine monthly household use values: [15, 30, 38, 45, 53, 64, 75, 77, 81]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 53, median 53.111, IQR 66.
  2. B. Mean 53.111, median 53, IQR 110.0.
  3. C. Mean 53.111, median 53, IQR 42.
  4. D. Mean 478, median 53, IQR 21.

Answer: C

The mean is 4789=53.111 and the median is the fifth ordered value, 53. Q1=34, Q3=76, so IQR=42. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 53, IQR 42. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 53, IQR 42. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 53, IQR 42. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 10. Exploring One-Variable Data

The school district in Metro East during a summer implementation review records nine lunch-program participation values: [14, 18, 32, 33, 55, 58, 64, 76, 77]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 47.444, median 55, IQR 95.
  2. B. Mean 47.444, median 55, IQR 45.
  3. C. Mean 427, median 55, IQR 22.5.
  4. D. Mean 55, median 47.444, IQR 63.

Answer: B

The mean is 4279=47.444 and the median is the fifth ordered value, 55. Q1=25, Q3=70, so IQR=45. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 47.444, median 55, IQR 45. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 47.444, median 55, IQR 45. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 47.444, median 55, IQR 45. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 11. Exploring One-Variable Data

The grocery cooperative in Cedar Grove during a pre-exam training cycle records nine checkout time values: [22, 31, 39, 47, 53, 67, 70, 73, 76]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 53, median 53.111, IQR 54.
  2. B. Mean 478, median 53, IQR 18.25.
  3. C. Mean 53.111, median 53, IQR 36.5.
  4. D. Mean 53.111, median 53, IQR 106.5.

Answer: C

The mean is 4789=53.111 and the median is the fifth ordered value, 53. Q1=35, Q3=71.5, so IQR=36.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 53, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 53, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 53.111, median 53, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 12. Exploring One-Variable Data

The housing authority in Sunbelt district during a randomized pilot period records nine application processing time values: [27, 29, 30, 32, 35, 46, 51, 60, 63]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 35, median 41.444, IQR 36.
  2. B. Mean 41.444, median 35, IQR 26.
  3. C. Mean 373, median 35, IQR 13.
  4. D. Mean 41.444, median 35, IQR 85.

Answer: B

The mean is 3739=41.444 and the median is the fifth ordered value, 35. Q1=29.5, Q3=55.5, so IQR=26. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 41.444, median 35, IQR 26. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 41.444, median 35, IQR 26. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 41.444, median 35, IQR 26. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 13. Exploring One-Variable Data

The community bank in Mountain Region during a summer implementation review records nine mobile-deposit adoption values: [12, 17, 18, 29, 36, 38, 59, 69, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 40, median 36, IQR 81.5.
  2. B. Mean 36, median 40, IQR 70.
  3. C. Mean 360, median 36, IQR 23.25.
  4. D. Mean 40, median 36, IQR 46.5.

Answer: D

The mean is 3609=40 and the median is the fifth ordered value, 36. Q1=17.5, Q3=64, so IQR=46.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 40, median 36, IQR 46.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 40, median 36, IQR 46.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 40, median 36, IQR 46.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 14. Exploring One-Variable Data

The municipal water office in Desert County during a spring 2027 pilot records nine monthly household use values: [16, 17, 20, 39, 43, 47, 66, 72, 78]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 44.222, median 43, IQR 50.5.
  2. B. Mean 398, median 43, IQR 25.25.
  3. C. Mean 44.222, median 43, IQR 87.5.
  4. D. Mean 43, median 44.222, IQR 62.

Answer: A

The mean is 3989=44.222 and the median is the fifth ordered value, 43. Q1=18.5, Q3=69, so IQR=50.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 44.222, median 43, IQR 50.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 44.222, median 43, IQR 50.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 44.222, median 43, IQR 50.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 15. Exploring One-Variable Data

The recycling program in Lakeside district during a follow-up evaluation period records nine weekly material weight values: [20, 36, 40, 43, 63, 69, 73, 78, 81]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 55.889, median 63, IQR 37.5.
  2. B. Mean 55.889, median 63, IQR 113.5.
  3. C. Mean 503, median 63, IQR 18.75.
  4. D. Mean 63, median 55.889, IQR 61.

Answer: A

The mean is 5039=55.889 and the median is the fifth ordered value, 63. Q1=38, Q3=75.5, so IQR=37.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 55.889, median 63, IQR 37.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 55.889, median 63, IQR 37.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 55.889, median 63, IQR 37.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 16. Exploring One-Variable Data

The school district in Westview during a service-improvement study records nine lunch-program participation values: [12, 28, 29, 30, 38, 45, 64, 74, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 38, median 44.667, IQR 70.
  2. B. Mean 44.667, median 38, IQR 40.5.
  3. C. Mean 44.667, median 38, IQR 97.5.
  4. D. Mean 402, median 38, IQR 20.25.

Answer: B

The mean is 4029=44.667 and the median is the fifth ordered value, 38. Q1=28.5, Q3=69, so IQR=40.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 44.667, median 38, IQR 40.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 44.667, median 38, IQR 40.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 44.667, median 38, IQR 40.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 17. Exploring One-Variable Data

The city recreation department in Desert County during a pre-exam training cycle records nine program satisfaction values: [13, 22, 28, 66, 69, 70, 71, 76, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 69, median 55, IQR 67.
  2. B. Mean 55, median 69, IQR 48.5.
  3. C. Mean 495, median 69, IQR 24.25.
  4. D. Mean 55, median 69, IQR 98.5.

Answer: B

The mean is 4959=55 and the median is the fifth ordered value, 69. Q1=25, Q3=73.5, so IQR=48.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 55, median 69, IQR 48.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 55, median 69, IQR 48.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 55, median 69, IQR 48.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 18. Exploring One-Variable Data

The municipal water office in Coastal Plains during a winter readiness review records nine monthly household use values: [20, 22, 32, 50, 53, 55, 58, 71, 83]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 49.333, median 53, IQR 91.5.
  2. B. Mean 444, median 53, IQR 18.75.
  3. C. Mean 49.333, median 53, IQR 37.5.
  4. D. Mean 53, median 49.333, IQR 63.

Answer: C

The mean is 4449=49.333 and the median is the fifth ordered value, 53. Q1=27, Q3=64.5, so IQR=37.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 49.333, median 53, IQR 37.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 49.333, median 53, IQR 37.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 49.333, median 53, IQR 37.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 19. Exploring One-Variable Data

The city recreation department in Capital Region during a regional benchmarking study records nine program satisfaction values: [15, 26, 27, 29, 33, 36, 39, 41, 64]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 34.444, median 33, IQR 66.5.
  2. B. Mean 310, median 33, IQR 6.75.
  3. C. Mean 33, median 34.444, IQR 49.
  4. D. Mean 34.444, median 33, IQR 13.5.

Answer: D

The mean is 3109=34.444 and the median is the fifth ordered value, 33. Q1=26.5, Q3=40, so IQR=13.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 34.444, median 33, IQR 13.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 34.444, median 33, IQR 13.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 34.444, median 33, IQR 13.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 20. Exploring One-Variable Data

The community college in Metro East during a summer implementation review records nine course completion values: [13, 27, 34, 35, 46, 55, 59, 66, 73]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 408, median 46, IQR 16.
  2. B. Mean 45.333, median 46, IQR 93.
  3. C. Mean 46, median 45.333, IQR 60.
  4. D. Mean 45.333, median 46, IQR 32.

Answer: D

The mean is 4089=45.333 and the median is the fifth ordered value, 46. Q1=30.5, Q3=62.5, so IQR=32. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 45.333, median 46, IQR 32. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 45.333, median 46, IQR 32. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 45.333, median 46, IQR 32. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 21. Exploring One-Variable Data

The city transit agency in Riverbend during a randomized pilot period records nine on-time arrival values: [16, 18, 20, 25, 50, 61, 66, 72, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 45.333, median 50, IQR 88.
  2. B. Mean 45.333, median 50, IQR 50.
  3. C. Mean 50, median 45.333, IQR 64.
  4. D. Mean 408, median 50, IQR 25.

Answer: B

The mean is 4089=45.333 and the median is the fifth ordered value, 50. Q1=19, Q3=69, so IQR=50. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 45.333, median 50, IQR 50. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 45.333, median 50, IQR 50. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 45.333, median 50, IQR 50. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 22. Exploring One-Variable Data

The public high school in Riverbend during a regional benchmarking study records nine algebra benchmark completion values: [12, 15, 28, 29, 33, 36, 63, 71, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 33, median 40.778, IQR 68.
  2. B. Mean 40.778, median 33, IQR 45.5.
  3. C. Mean 367, median 33, IQR 22.75.
  4. D. Mean 40.778, median 33, IQR 88.5.

Answer: B

The mean is 3679=40.778 and the median is the fifth ordered value, 33. Q1=21.5, Q3=67, so IQR=45.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 40.778, median 33, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 40.778, median 33, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 40.778, median 33, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 23. Exploring One-Variable Data

The county election office in Prairie District during a summer implementation review records nine ballot-processing time values: [14, 29, 37, 39, 40, 72, 74, 75, 78]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 40, median 50.889, IQR 64.
  2. B. Mean 50.889, median 40, IQR 41.5.
  3. C. Mean 50.889, median 40, IQR 107.5.
  4. D. Mean 458, median 40, IQR 20.75.

Answer: B

The mean is 4589=50.889 and the median is the fifth ordered value, 40. Q1=33, Q3=74.5, so IQR=41.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 50.889, median 40, IQR 41.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 50.889, median 40, IQR 41.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 50.889, median 40, IQR 41.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 24. Exploring One-Variable Data

The public health department in Capital Region during a baseline measurement week records nine vaccination appointment completion values: [27, 40, 44, 47, 49, 51, 62, 63, 68]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 49, median 50.111, IQR 41.
  2. B. Mean 50.111, median 49, IQR 20.5.
  3. C. Mean 50.111, median 49, IQR 104.5.
  4. D. Mean 451, median 49, IQR 10.25.

Answer: B

The mean is 4519=50.111 and the median is the fifth ordered value, 49. Q1=42, Q3=62.5, so IQR=20.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 50.111, median 49, IQR 20.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 50.111, median 49, IQR 20.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 50.111, median 49, IQR 20.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 25. Exploring One-Variable Data

The municipal emergency dispatch center in Riverbend during a spring 2027 pilot records nine response time values: [12, 21, 38, 39, 52, 56, 58, 75, 79]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 52, median 47.778, IQR 67.
  2. B. Mean 430, median 52, IQR 18.5.
  3. C. Mean 47.778, median 52, IQR 96.
  4. D. Mean 47.778, median 52, IQR 37.

Answer: D

The mean is 4309=47.778 and the median is the fifth ordered value, 52. Q1=29.5, Q3=66.5, so IQR=37. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 47.778, median 52, IQR 37. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 47.778, median 52, IQR 37. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 47.778, median 52, IQR 37. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 26. Exploring One-Variable Data

The community college in Sunbelt district during a school-year data collection records nine course completion values: [13, 15, 16, 24, 33, 35, 36, 55, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 33, median 34.333, IQR 69.
  2. B. Mean 34.333, median 33, IQR 30.
  3. C. Mean 309, median 33, IQR 15.
  4. D. Mean 34.333, median 33, IQR 61.

Answer: B

The mean is 3099=34.333 and the median is the fifth ordered value, 33. Q1=15.5, Q3=45.5, so IQR=30. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 34.333, median 33, IQR 30. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 34.333, median 33, IQR 30. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 34.333, median 33, IQR 30. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 27. Exploring One-Variable Data

The regional airport authority in Coastal Plains during a two-month observation window records nine security wait time values: [16, 17, 21, 40, 41, 59, 63, 66, 78]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 41, median 44.556, IQR 62.
  2. B. Mean 44.556, median 41, IQR 45.5.
  3. C. Mean 401, median 41, IQR 22.75.
  4. D. Mean 44.556, median 41, IQR 83.5.

Answer: B

The mean is 4019=44.556 and the median is the fifth ordered value, 41. Q1=19, Q3=64.5, so IQR=45.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 44.556, median 41, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 44.556, median 41, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 44.556, median 41, IQR 45.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 28. Exploring One-Variable Data

The farm cooperative in Desert County during a follow-up evaluation period records nine crop yield values: [15, 16, 31, 36, 45, 47, 57, 63, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 43.556, median 45, IQR 83.5.
  2. B. Mean 45, median 43.556, IQR 67.
  3. C. Mean 43.556, median 45, IQR 36.5.
  4. D. Mean 392, median 45, IQR 18.25.

Answer: C

The mean is 3929=43.556 and the median is the fifth ordered value, 45. Q1=23.5, Q3=60, so IQR=36.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 43.556, median 45, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 43.556, median 45, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 43.556, median 45, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 29. Exploring One-Variable Data

The solar installer in New England network during a multiweek validation study records nine daily energy output values: [12, 35, 42, 45, 51, 64, 69, 72, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 470, median 51, IQR 16.
  2. B. Mean 52.222, median 51, IQR 32.
  3. C. Mean 52.222, median 51, IQR 109.0.
  4. D. Mean 51, median 52.222, IQR 68.

Answer: B

The mean is 4709=52.222 and the median is the fifth ordered value, 51. Q1=38.5, Q3=70.5, so IQR=32. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 52.222, median 51, IQR 32. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 52.222, median 51, IQR 32. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 52.222, median 51, IQR 32. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 30. Exploring One-Variable Data

The grocery cooperative in Pine Ridge during a baseline measurement week records nine checkout time values: [18, 21, 22, 30, 36, 43, 51, 65, 78]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 364, median 36, IQR 18.25.
  2. B. Mean 40.444, median 36, IQR 36.5.
  3. C. Mean 36, median 40.444, IQR 60.
  4. D. Mean 40.444, median 36, IQR 79.5.

Answer: B

The mean is 3649=40.444 and the median is the fifth ordered value, 36. Q1=21.5, Q3=58, so IQR=36.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 40.444, median 36, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 40.444, median 36, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 40.444, median 36, IQR 36.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 31. Exploring One-Variable Data

The public health department in Desert County during a quarterly performance study records nine vaccination appointment completion values: [19, 22, 31, 34, 40, 57, 64, 78, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 47.444, median 40, IQR 44.5.
  2. B. Mean 47.444, median 40, IQR 97.5.
  3. C. Mean 427, median 40, IQR 22.25.
  4. D. Mean 40, median 47.444, IQR 63.

Answer: A

The mean is 4279=47.444 and the median is the fifth ordered value, 40. Q1=26.5, Q3=71, so IQR=44.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 47.444, median 40, IQR 44.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 47.444, median 40, IQR 44.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 47.444, median 40, IQR 44.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 32. Exploring One-Variable Data

The school district in Midwest consortium during a follow-up evaluation period records nine lunch-program participation values: [18, 25, 29, 40, 50, 54, 64, 71, 74]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 50, median 47.222, IQR 56.
  2. B. Mean 47.222, median 50, IQR 94.5.
  3. C. Mean 47.222, median 50, IQR 40.5.
  4. D. Mean 425, median 50, IQR 20.25.

Answer: C

The mean is 4259=47.222 and the median is the fifth ordered value, 50. Q1=27, Q3=67.5, so IQR=40.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 47.222, median 50, IQR 40.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 47.222, median 50, IQR 40.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 47.222, median 50, IQR 40.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 33. Exploring One-Variable Data

The solar installer in Pacific Northwest during a follow-up evaluation period records nine daily energy output values: [27, 38, 52, 60, 61, 64, 74, 76, 77]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 58.778, median 61, IQR 30.
  2. B. Mean 61, median 58.778, IQR 50.
  3. C. Mean 529, median 61, IQR 15.
  4. D. Mean 58.778, median 61, IQR 120.0.

Answer: A

The mean is 5299=58.778 and the median is the fifth ordered value, 61. Q1=45, Q3=75, so IQR=30. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 58.778, median 61, IQR 30. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 58.778, median 61, IQR 30. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 58.778, median 61, IQR 30. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 34. Exploring One-Variable Data

The digital learning platform in Pine Ridge during a two-month observation window records nine lesson completion values: [15, 16, 37, 40, 41, 46, 53, 71, 79]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 41, median 44.222, IQR 64.
  2. B. Mean 398, median 41, IQR 17.75.
  3. C. Mean 44.222, median 41, IQR 88.5.
  4. D. Mean 44.222, median 41, IQR 35.5.

Answer: D

The mean is 3989=44.222 and the median is the fifth ordered value, 41. Q1=26.5, Q3=62, so IQR=35.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 44.222, median 41, IQR 35.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 44.222, median 41, IQR 35.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 44.222, median 41, IQR 35.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 35. Exploring One-Variable Data

The farm cooperative in Cedar Grove during a multiweek validation study records nine crop yield values: [20, 39, 49, 58, 63, 66, 70, 79, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 524, median 63, IQR 15.25.
  2. B. Mean 63, median 58.222, IQR 60.
  3. C. Mean 58.222, median 63, IQR 118.5.
  4. D. Mean 58.222, median 63, IQR 30.5.

Answer: D

The mean is 5249=58.222 and the median is the fifth ordered value, 63. Q1=44, Q3=74.5, so IQR=30.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 58.222, median 63, IQR 30.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 58.222, median 63, IQR 30.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice C: It does not match the requested calculation. The correct comparison or result is: Mean 58.222, median 63, IQR 30.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Question 36. Exploring One-Variable Data

The housing authority in Midwest consortium during a two-month observation window records nine application processing time values: [33, 35, 36, 38, 43, 47, 54, 60, 79]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. A. Mean 425, median 43, IQR 10.75.
  2. B. Mean 47.222, median 43, IQR 92.5.
  3. C. Mean 47.222, median 43, IQR 21.5.
  4. D. Mean 43, median 47.222, IQR 46.

Answer: C

The mean is 4259=47.222 and the median is the fifth ordered value, 43. Q1=35.5, Q3=57, so IQR=21.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Why the other choices fail

  • Choice A: It does not match the requested calculation. The correct comparison or result is: Mean 47.222, median 43, IQR 21.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice B: It does not match the requested calculation. The correct comparison or result is: Mean 47.222, median 43, IQR 21.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.
  • Choice D: It does not match the requested calculation. The correct comparison or result is: Mean 47.222, median 43, IQR 21.5. Key check: Mean and standard deviation are nonresistant; median and IQR are resistant.

Exploring One-Variable Data free-response practice

10-point analytic study rubric used for the sets below
EvidencePoints
Correct target, notation, direction, or group order2
Correct method/model and defensible conditions2
Correct setup and execution3
Contextual interpretation and scope/limitation2
Clear communication with units and labels1

FRQ set 1: Exploring One-Variable Data

Scenario. The public health department in North Valley during a fall 2026 audit records nine vaccination appointment completion values: [26, 28, 29, 30, 55, 56, 60, 67, 73]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4249=47.111 and the median is the fifth ordered value, 55. Q1=28.5, Q3=63.5, so IQR=35. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 2: Exploring One-Variable Data

Scenario. The solar installer in Riverbend during a school-year data collection records nine daily energy output values: [19, 20, 26, 43, 49, 58, 64, 65, 84]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4289=47.556 and the median is the fifth ordered value, 49. Q1=23, Q3=64.5, so IQR=41.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 3: Exploring One-Variable Data

Scenario. The food safety laboratory in Lakeside district during a semester-long cohort study records nine sample concentration values: [13, 19, 24, 33, 48, 49, 52, 56, 80]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 3749=41.556 and the median is the fifth ordered value, 48. Q1=21.5, Q3=54, so IQR=32.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 4: Exploring One-Variable Data

Scenario. The digital learning platform in New England network during a monthly quality review records nine lesson completion values: [22, 26, 47, 49, 66, 74, 75, 79, 84]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 5229=58 and the median is the fifth ordered value, 66. Q1=36.5, Q3=77, so IQR=40.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 5: Exploring One-Variable Data

Scenario. The housing authority in Central County during a randomized pilot period records nine application processing time values: [18, 20, 35, 46, 50, 63, 74, 79, 81]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4669=51.778 and the median is the fifth ordered value, 50. Q1=27.5, Q3=76.5, so IQR=49. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 6: Exploring One-Variable Data

Scenario. The wildlife clinic in Desert County during a weekday operations study records nine recovery time values: [16, 17, 31, 35, 45, 50, 51, 52, 66]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 3639=40.333 and the median is the fifth ordered value, 45. Q1=24, Q3=51.5, so IQR=27.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 7: Exploring One-Variable Data

Scenario. The municipal emergency dispatch center in Metro East during a school-year data collection records nine response time values: [16, 28, 37, 40, 41, 47, 50, 53, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 3949=43.778 and the median is the fifth ordered value, 41. Q1=32.5, Q3=51.5, so IQR=19. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 8: Exploring One-Variable Data

Scenario. The city transit agency in Mountain Region during a semester-long cohort study records nine on-time arrival values: [13, 25, 28, 42, 50, 68, 75, 78, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4619=51.222 and the median is the fifth ordered value, 50. Q1=26.5, Q3=76.5, so IQR=50. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 9: Exploring One-Variable Data

Scenario. The university advising center in Riverbend during a winter readiness review records nine appointment wait time values: [13, 25, 38, 44, 49, 57, 66, 69, 83]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4449=49.333 and the median is the fifth ordered value, 49. Q1=31.5, Q3=67.5, so IQR=36. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 10: Exploring One-Variable Data

Scenario. The public health department in Midwest consortium during a multiweek validation study records nine vaccination appointment completion values: [23, 37, 49, 56, 58, 67, 70, 78, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 5209=57.778 and the median is the fifth ordered value, 58. Q1=43, Q3=74, so IQR=31. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 11: Exploring One-Variable Data

Scenario. The housing authority in Midwest consortium during a baseline measurement week records nine application processing time values: [26, 39, 57, 64, 68, 75, 76, 80, 82]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 5679=63 and the median is the fifth ordered value, 68. Q1=48, Q3=78, so IQR=30. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 12: Exploring One-Variable Data

Scenario. The community bank in Cedar Grove during a baseline measurement week records nine mobile-deposit adoption values: [15, 24, 30, 48, 53, 61, 62, 74, 81]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4489=49.778 and the median is the fifth ordered value, 53. Q1=27, Q3=68, so IQR=41. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 13: Exploring One-Variable Data

Scenario. The regional manufacturer in Prairie District during a six-week field trial records nine part diameter values: [30, 33, 36, 40, 46, 53, 55, 67, 79]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4399=48.778 and the median is the fifth ordered value, 46. Q1=34.5, Q3=61, so IQR=26.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

FRQ set 14: Exploring One-Variable Data

Scenario. The public health department in Riverbend during a monthly quality review records nine vaccination appointment completion values: [20, 21, 23, 28, 51, 57, 70, 71, 81]. Calculate the mean, median, and IQR, then describe what each contributes to a distribution summary.

  1. Define the variable, units, groups, and requested distribution or model feature.
  2. Show the required calculation or graphical/model reasoning with labeled quantities.
  3. Interpret the numerical result in the context of the data rather than as an isolated number.
  4. Identify an unusual feature, limitation, or condition that affects the conclusion.

Model response

The mean is 4229=46.889 and the median is the fifth ordered value, 51. Q1=22, Q3=70.5, so IQR=48.5. Mean uses every value and is sensitive to extremes; median and IQR are resistant summaries of center and middle-half spread.

Continue AP Statistics practice

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Engr. Muhammad Yar Saqib author profile photo

Engr. Muhammad Yar Saqib

Engr. Muhammad Yar Saqib is an electrical engineer educated at the University of Bradford, United Kingdom, a writer and poet, and an Assistant Education Officer in the School Education Department, Punjab, serving since July 2017. He writes practical guides on statistics, SPSS, data analysis, mathematics and educational technology, with an emphasis on transparent methods, reproducible calculations and ethical learning support.

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