What does Frequency and Relative Frequency Tables measure or decide?

Relative frequency equals category frequency divided by the total count.

When should I use Frequency and Relative Frequency Tables?

Use one denominator consistently and distinguish counts from proportions.

Which conditions or design checks matter for Frequency and Relative Frequency Tables?

Verify mutually exclusive categories, one consistent total, and the correct denominator before converting counts to proportions or percentages.

Which formula or calculator output matters most for Frequency and Relative Frequency Tables?

Use relative frequency=category count/total count and keep the denominator visible.

How should results from Frequency and Relative Frequency Tables be interpreted?

Name the population, process, groups, variable, and units from the prompt. Then explain what the calculated value or design result means without claiming causation or generalization beyond what the study supports.

What mistake most often changes the answer in Frequency and Relative Frequency Tables?

The most damaging error is solving a nearby question with a different denominator, group order, tail, parameter, standard error, or scope. Use this correction rule: Use one denominator consistently and distinguish counts from proportions.

Are the questions on this Frequency and Relative Frequency Tables page copied from past AP exams?

No. Released AP Statistics materials are used to identify authentic skills and response demands. Every Frequency and Relative Frequency Tables practice item here is an original parallel problem with changed data, context, target, and solution.

Is Frequency and Relative Frequency Tables required for the May 2027 AP Statistics exam?

Yes. Frequency and Relative Frequency Tables is included in the current five-unit course and is linked here to Unit 1 practice, formulas, MCQs, and FRQs.

Frequency and Relative Frequency Tables: AP Statistics Guide

AP Statistics Practice

Frequency and Relative Frequency Tables: AP Statistics Guide

Frequency and Relative Frequency Tables: AP Statistics Guide 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

Frequency and Relative Frequency Tables: AP Statistics Guide: formulas and targets

Relative frequency	category count ÷ total count
Percent	relative frequency × 100%

Frequency and Relative Frequency Tables multiple-choice practice

Question 1. Frequency and Relative Frequency Tables

For four categories of lunch-program participation at a school district in South Harbor during a quarterly performance study, observed counts are [36, 55, 63, 57]. Find the relative frequency for category 2 and state its meaning.

A. 55; relative frequency is reported as the original count.
B. 0.261; about 26.1% of the observed units are in category 2.
C. 3.836; divide the total by the category count.
D. 0.55; always divide a count by 100.

Answer: B

The total is 211. Category 2 has relative frequency 55211=0.261, so 26.1% of the observed students were in category 2.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.261; about 26.1% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.261; about 26.1% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.261; about 26.1% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 2. Frequency and Relative Frequency Tables

For four categories of monthly household use at a municipal water office in Westview during a follow-up evaluation period, observed counts are [65, 47, 44, 20]. Find the relative frequency for category 2 and state its meaning.

A. 3.745; divide the total by the category count.
B. 0.267; about 26.7% of the observed units are in category 2.
C. 0.47; always divide a count by 100.
D. 47; relative frequency is reported as the original count.

Answer: B

The total is 176. Category 2 has relative frequency 47176=0.267, so 26.7% of the observed accounts were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.267; about 26.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.267; about 26.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.267; about 26.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 3. Frequency and Relative Frequency Tables

For four categories of appointment wait time at a university advising center in North Valley during a randomized pilot period, observed counts are [26, 58, 63, 20]. Find the relative frequency for category 1 and state its meaning.

A. 26; relative frequency is reported as the original count.
B. 0.26; always divide a count by 100.
C. 0.156; about 15.6% of the observed units are in category 1.
D. 6.423; divide the total by the category count.

Answer: C

The total is 167. Category 1 has relative frequency 26167=0.156, so 15.6% of the observed appointments were in category 1.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.156; about 15.6% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.156; about 15.6% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.156; about 15.6% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 4. Frequency and Relative Frequency Tables

For four categories of program satisfaction at a city recreation department in Metro East during a six-week field trial, observed counts are [26, 28, 43, 27]. Find the relative frequency for category 1 and state its meaning.

A. 4.769; divide the total by the category count.
B. 0.21; about 21.0% of the observed units are in category 1.
C. 0.26; always divide a count by 100.
D. 26; relative frequency is reported as the original count.

Answer: B

The total is 124. Category 1 has relative frequency 26124=0.21, so 21.0% of the observed participants were in category 1.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.21; about 21.0% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.21; about 21.0% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.21; about 21.0% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 5. Frequency and Relative Frequency Tables

For four categories of weekly material weight at a recycling program in South Harbor during a randomized pilot period, observed counts are [35, 47, 20, 62]. Find the relative frequency for category 2 and state its meaning.

A. 0.47; always divide a count by 100.
B. 47; relative frequency is reported as the original count.
C. 3.489; divide the total by the category count.
D. 0.287; about 28.7% of the observed units are in category 2.

Answer: D

The total is 164. Category 2 has relative frequency 47164=0.287, so 28.7% of the observed households were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.287; about 28.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.287; about 28.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.287; about 28.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 6. Frequency and Relative Frequency Tables

For four categories of recovery time at a wildlife clinic in Desert County during a spring 2027 pilot, observed counts are [38, 61, 30, 64]. Find the relative frequency for category 1 and state its meaning.

A. 38; relative frequency is reported as the original count.
B. 5.079; divide the total by the category count.
C. 0.38; always divide a count by 100.
D. 0.197; about 19.7% of the observed units are in category 1.

Answer: D

The total is 193. Category 1 has relative frequency 38193=0.197, so 19.7% of the observed animals were in category 1.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.197; about 19.7% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.197; about 19.7% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.197; about 19.7% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 7. Frequency and Relative Frequency Tables

For four categories of ballot-processing time at a county election office in New England network during a monthly quality review, observed counts are [41, 30, 18, 21]. Find the relative frequency for category 4 and state its meaning.

A. 0.191; about 19.1% of the observed units are in category 4.
B. 0.21; always divide a count by 100.
C. 5.238; divide the total by the category count.
D. 21; relative frequency is reported as the original count.

Answer: A

The total is 110. Category 4 has relative frequency 21110=0.191, so 19.1% of the observed ballots were in category 4.

Why the other choices fail

Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.191; about 19.1% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.191; about 19.1% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.191; about 19.1% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.

Question 8. Frequency and Relative Frequency Tables

For four categories of lesson completion at a digital learning platform in Central County during a spring 2027 pilot, observed counts are [53, 56, 36, 53]. Find the relative frequency for category 3 and state its meaning.

A. 36; relative frequency is reported as the original count.
B. 0.182; about 18.2% of the observed units are in category 3.
C. 0.36; always divide a count by 100.
D. 5.5; divide the total by the category count.

Answer: B

The total is 198. Category 3 has relative frequency 36198=0.182, so 18.2% of the observed learners were in category 3.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.182; about 18.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.182; about 18.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.182; about 18.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 9. Frequency and Relative Frequency Tables

For four categories of response time at a municipal emergency dispatch center in Cedar Grove during a spring 2027 pilot, observed counts are [27, 29, 21, 20]. Find the relative frequency for category 1 and state its meaning.

A. 3.593; divide the total by the category count.
B. 0.278; about 27.8% of the observed units are in category 1.
C. 0.27; always divide a count by 100.
D. 27; relative frequency is reported as the original count.

Answer: B

The total is 97. Category 1 has relative frequency 2797=0.278, so 27.8% of the observed calls were in category 1.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.278; about 27.8% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.278; about 27.8% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.278; about 27.8% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 10. Frequency and Relative Frequency Tables

For four categories of mobile-deposit adoption at a community bank in North Valley during a randomized pilot period, observed counts are [29, 50, 18, 43]. Find the relative frequency for category 4 and state its meaning.

A. 0.43; always divide a count by 100.
B. 43; relative frequency is reported as the original count.
C. 0.307; about 30.7% of the observed units are in category 4.
D. 3.256; divide the total by the category count.

Answer: C

The total is 140. Category 4 has relative frequency 43140=0.307, so 30.7% of the observed customers were in category 4.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.307; about 30.7% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.307; about 30.7% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.307; about 30.7% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.

Question 11. Frequency and Relative Frequency Tables

For four categories of trail-use duration at a state park in New England network during a six-week field trial, observed counts are [24, 32, 31, 23]. Find the relative frequency for category 3 and state its meaning.

A. 0.31; always divide a count by 100.
B. 3.548; divide the total by the category count.
C. 31; relative frequency is reported as the original count.
D. 0.282; about 28.2% of the observed units are in category 3.

Answer: D

The total is 110. Category 3 has relative frequency 31110=0.282, so 28.2% of the observed visitors were in category 3.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.282; about 28.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.282; about 28.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It does not match the requested calculation. The correct comparison or result is: 0.282; about 28.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 12. Frequency and Relative Frequency Tables

For four categories of weekly material weight at a recycling program in Sunbelt district during a weekday operations study, observed counts are [55, 58, 56, 60]. Find the relative frequency for category 2 and state its meaning.

A. 3.948; divide the total by the category count.
B. 0.253; about 25.3% of the observed units are in category 2.
C. 0.58; always divide a count by 100.
D. 58; relative frequency is reported as the original count.

Answer: B

The total is 229. Category 2 has relative frequency 58229=0.253, so 25.3% of the observed households were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.253; about 25.3% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.253; about 25.3% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.253; about 25.3% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 13. Frequency and Relative Frequency Tables

For four categories of lunch-program participation at a school district in Riverbend during a spring 2027 pilot, observed counts are [60, 26, 43, 40]. Find the relative frequency for category 3 and state its meaning.

A. 3.93; divide the total by the category count.
B. 0.254; about 25.4% of the observed units are in category 3.
C. 43; relative frequency is reported as the original count.
D. 0.43; always divide a count by 100.

Answer: B

The total is 169. Category 3 has relative frequency 43169=0.254, so 25.4% of the observed students were in category 3.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.254; about 25.4% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It does not match the requested calculation. The correct comparison or result is: 0.254; about 25.4% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.254; about 25.4% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 14. Frequency and Relative Frequency Tables

For four categories of recovery time at a wildlife clinic in Pine Ridge during a quarterly performance study, observed counts are [61, 33, 37, 54]. Find the relative frequency for category 3 and state its meaning.

A. 0.37; always divide a count by 100.
B. 37; relative frequency is reported as the original count.
C. 0.2; about 20.0% of the observed units are in category 3.
D. 5; divide the total by the category count.

Answer: C

The total is 185. Category 3 has relative frequency 37185=0.2, so 20.0% of the observed animals were in category 3.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.2; about 20.0% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.2; about 20.0% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.2; about 20.0% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 15. Frequency and Relative Frequency Tables

For four categories of trail-use duration at a state park in Westview during a six-week field trial, observed counts are [42, 51, 29, 47]. Find the relative frequency for category 1 and state its meaning.

A. 4.024; divide the total by the category count.
B. 42; relative frequency is reported as the original count.
C. 0.249; about 24.9% of the observed units are in category 1.
D. 0.42; always divide a count by 100.

Answer: C

The total is 169. Category 1 has relative frequency 42169=0.249, so 24.9% of the observed visitors were in category 1.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.249; about 24.9% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.249; about 24.9% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.249; about 24.9% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 16. Frequency and Relative Frequency Tables

For four categories of response time at a municipal emergency dispatch center in Riverbend during a quarterly performance study, observed counts are [54, 25, 35, 54]. Find the relative frequency for category 4 and state its meaning.

A. 54; relative frequency is reported as the original count.
B. 0.54; always divide a count by 100.
C. 0.321; about 32.1% of the observed units are in category 4.
D. 3.111; divide the total by the category count.

Answer: C

The total is 168. Category 4 has relative frequency 54168=0.321, so 32.1% of the observed calls were in category 4.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.321; about 32.1% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.321; about 32.1% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.321; about 32.1% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.

Question 17. Frequency and Relative Frequency Tables

For four categories of algebra benchmark completion at a public high school in Lakeside district during a monthly quality review, observed counts are [56, 51, 50, 63]. Find the relative frequency for category 1 and state its meaning.

A. 0.255; about 25.5% of the observed units are in category 1.
B. 0.56; always divide a count by 100.
C. 56; relative frequency is reported as the original count.
D. 3.929; divide the total by the category count.

Answer: A

The total is 220. Category 1 has relative frequency 56220=0.255, so 25.5% of the observed students were in category 1.

Why the other choices fail

Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.255; about 25.5% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It does not match the requested calculation. The correct comparison or result is: 0.255; about 25.5% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.255; about 25.5% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 18. Frequency and Relative Frequency Tables

For four categories of appointment completion at a regional hospital in Atlantic Corridor during a service-improvement study, observed counts are [55, 42, 64, 59]. Find the relative frequency for category 2 and state its meaning.

A. 0.42; always divide a count by 100.
B. 5.238; divide the total by the category count.
C. 0.191; about 19.1% of the observed units are in category 2.
D. 42; relative frequency is reported as the original count.

Answer: C

The total is 220. Category 2 has relative frequency 42220=0.191, so 19.1% of the observed patients were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.191; about 19.1% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.191; about 19.1% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.191; about 19.1% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 19. Frequency and Relative Frequency Tables

For four categories of daily energy output at a solar installer in Cedar Grove during a monthly quality review, observed counts are [60, 21, 35, 26]. Find the relative frequency for category 3 and state its meaning.

A. 0.246; about 24.6% of the observed units are in category 3.
B. 35; relative frequency is reported as the original count.
C. 0.35; always divide a count by 100.
D. 4.057; divide the total by the category count.

Answer: A

The total is 142. Category 3 has relative frequency 35142=0.246, so 24.6% of the observed installations were in category 3.

Why the other choices fail

Choice B: It does not match the requested calculation. The correct comparison or result is: 0.246; about 24.6% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.246; about 24.6% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.246; about 24.6% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 20. Frequency and Relative Frequency Tables

For four categories of checkout time at a grocery cooperative in North Valley during a community outreach cycle, observed counts are [48, 48, 59, 27]. Find the relative frequency for category 2 and state its meaning.

A. 3.792; divide the total by the category count.
B. 48; relative frequency is reported as the original count.
C. 0.264; about 26.4% of the observed units are in category 2.
D. 0.48; always divide a count by 100.

Answer: C

The total is 182. Category 2 has relative frequency 48182=0.264, so 26.4% of the observed customers were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.264; about 26.4% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.264; about 26.4% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.264; about 26.4% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 21. Frequency and Relative Frequency Tables

For four categories of monthly household use at a municipal water office in Desert County during a monthly quality review, observed counts are [60, 22, 25, 54]. Find the relative frequency for category 2 and state its meaning.

A. 7.318; divide the total by the category count.
B. 22; relative frequency is reported as the original count.
C. 0.22; always divide a count by 100.
D. 0.137; about 13.7% of the observed units are in category 2.

Answer: D

The total is 161. Category 2 has relative frequency 22161=0.137, so 13.7% of the observed accounts were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.137; about 13.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.137; about 13.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.137; about 13.7% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 22. Frequency and Relative Frequency Tables

For four categories of program satisfaction at a city recreation department in Desert County during a fall 2026 audit, observed counts are [33, 62, 53, 62]. Find the relative frequency for category 4 and state its meaning.

A. 3.387; divide the total by the category count.
B. 62; relative frequency is reported as the original count.
C. 0.62; always divide a count by 100.
D. 0.295; about 29.5% of the observed units are in category 4.

Answer: D

The total is 210. Category 4 has relative frequency 62210=0.295, so 29.5% of the observed participants were in category 4.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.295; about 29.5% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.295; about 29.5% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.295; about 29.5% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.

Question 23. Frequency and Relative Frequency Tables

For four categories of on-time arrival at a city transit agency in Midwest consortium during a school-year data collection, observed counts are [41, 49, 41, 46]. Find the relative frequency for category 4 and state its meaning.

A. 46; relative frequency is reported as the original count.
B. 3.848; divide the total by the category count.
C. 0.46; always divide a count by 100.
D. 0.26; about 26.0% of the observed units are in category 4.

Answer: D

The total is 177. Category 4 has relative frequency 46177=0.26, so 26.0% of the observed bus trips were in category 4.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.26; about 26.0% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.26; about 26.0% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.26; about 26.0% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.

Question 24. Frequency and Relative Frequency Tables

For four categories of daily energy output at a solar installer in Coastal Plains during a spring 2027 pilot, observed counts are [60, 20, 65, 30]. Find the relative frequency for category 3 and state its meaning.

A. 0.371; about 37.1% of the observed units are in category 3.
B. 2.692; divide the total by the category count.
C. 0.65; always divide a count by 100.
D. 65; relative frequency is reported as the original count.

Answer: A

The total is 175. Category 3 has relative frequency 65175=0.371, so 37.1% of the observed installations were in category 3.

Why the other choices fail

Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.371; about 37.1% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.371; about 37.1% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.371; about 37.1% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 25. Frequency and Relative Frequency Tables

For four categories of program satisfaction at a city recreation department in Capital Region during a yearly program evaluation, observed counts are [27, 43, 37, 46]. Find the relative frequency for category 3 and state its meaning.

A. 4.135; divide the total by the category count.
B. 37; relative frequency is reported as the original count.
C. 0.242; about 24.2% of the observed units are in category 3.
D. 0.37; always divide a count by 100.

Answer: C

The total is 153. Category 3 has relative frequency 37153=0.242, so 24.2% of the observed participants were in category 3.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.242; about 24.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.242; about 24.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.242; about 24.2% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 26. Frequency and Relative Frequency Tables

For four categories of security wait time at a regional airport authority in Sunbelt district during a six-week field trial, observed counts are [19, 59, 29, 32]. Find the relative frequency for category 1 and state its meaning.

A. 7.316; divide the total by the category count.
B. 0.137; about 13.7% of the observed units are in category 1.
C. 0.19; always divide a count by 100.
D. 19; relative frequency is reported as the original count.

Answer: B

The total is 139. Category 1 has relative frequency 19139=0.137, so 13.7% of the observed travelers were in category 1.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.137; about 13.7% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.137; about 13.7% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It does not match the requested calculation. The correct comparison or result is: 0.137; about 13.7% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 27. Frequency and Relative Frequency Tables

For four categories of lesson completion at a digital learning platform in Capital Region during a randomized pilot period, observed counts are [26, 18, 23, 36]. Find the relative frequency for category 3 and state its meaning.

A. 0.23; always divide a count by 100.
B. 0.223; about 22.3% of the observed units are in category 3.
C. 23; relative frequency is reported as the original count.
D. 4.478; divide the total by the category count.

Answer: B

The total is 103. Category 3 has relative frequency 23103=0.223, so 22.3% of the observed learners were in category 3.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.223; about 22.3% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It does not match the requested calculation. The correct comparison or result is: 0.223; about 22.3% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.223; about 22.3% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 28. Frequency and Relative Frequency Tables

For four categories of sample concentration at a food safety laboratory in Cedar Grove during a quarterly performance study, observed counts are [35, 20, 21, 49]. Find the relative frequency for category 3 and state its meaning.

A. 21; relative frequency is reported as the original count.
B. 0.21; always divide a count by 100.
C. 0.168; about 16.8% of the observed units are in category 3.
D. 5.952; divide the total by the category count.

Answer: C

The total is 125. Category 3 has relative frequency 21125=0.168, so 16.8% of the observed samples were in category 3.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.168; about 16.8% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.168; about 16.8% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.168; about 16.8% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 29. Frequency and Relative Frequency Tables

For four categories of weekly material weight at a recycling program in Westview during a weekday operations study, observed counts are [36, 45, 53, 54]. Find the relative frequency for category 4 and state its meaning.

A. 54; relative frequency is reported as the original count.
B. 0.54; always divide a count by 100.
C. 0.287; about 28.7% of the observed units are in category 4.
D. 3.481; divide the total by the category count.

Answer: C

The total is 188. Category 4 has relative frequency 54188=0.287, so 28.7% of the observed households were in category 4.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.287; about 28.7% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.287; about 28.7% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.287; about 28.7% of the observed units are in category 4. Key check: Relative frequency equals category frequency divided by the total count.

Question 30. Frequency and Relative Frequency Tables

For four categories of daily energy output at a solar installer in Pine Ridge during a semester-long cohort study, observed counts are [38, 27, 34, 49]. Find the relative frequency for category 2 and state its meaning.

A. 27; relative frequency is reported as the original count.
B. 5.481; divide the total by the category count.
C. 0.27; always divide a count by 100.
D. 0.182; about 18.2% of the observed units are in category 2.

Answer: D

The total is 148. Category 2 has relative frequency 27148=0.182, so 18.2% of the observed installations were in category 2.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.182; about 18.2% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.182; about 18.2% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.182; about 18.2% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 31. Frequency and Relative Frequency Tables

For four categories of appointment wait time at a university advising center in Cedar Grove during a semester-long cohort study, observed counts are [25, 60, 30, 18]. Find the relative frequency for category 1 and state its meaning.

A. 25; relative frequency is reported as the original count.
B. 5.32; divide the total by the category count.
C. 0.188; about 18.8% of the observed units are in category 1.
D. 0.25; always divide a count by 100.

Answer: C

The total is 133. Category 1 has relative frequency 25133=0.188, so 18.8% of the observed appointments were in category 1.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.188; about 18.8% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.188; about 18.8% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.188; about 18.8% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 32. Frequency and Relative Frequency Tables

For four categories of weekly material weight at a recycling program in Pacific Northwest during a follow-up evaluation period, observed counts are [19, 25, 60, 48]. Find the relative frequency for category 1 and state its meaning.

A. 19; relative frequency is reported as the original count.
B. 0.125; about 12.5% of the observed units are in category 1.
C. 0.19; always divide a count by 100.
D. 8; divide the total by the category count.

Answer: B

The total is 152. Category 1 has relative frequency 19152=0.125, so 12.5% of the observed households were in category 1.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.125; about 12.5% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.125; about 12.5% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.125; about 12.5% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Question 33. Frequency and Relative Frequency Tables

For four categories of security wait time at a regional airport authority in Mountain Region during a semester-long cohort study, observed counts are [30, 28, 19, 59]. Find the relative frequency for category 2 and state its meaning.

A. 4.857; divide the total by the category count.
B. 28; relative frequency is reported as the original count.
C. 0.206; about 20.6% of the observed units are in category 2.
D. 0.28; always divide a count by 100.

Answer: C

The total is 136. Category 2 has relative frequency 28136=0.206, so 20.6% of the observed travelers were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.206; about 20.6% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.206; about 20.6% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.206; about 20.6% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 34. Frequency and Relative Frequency Tables

For four categories of ballot-processing time at a county election office in South Harbor during a baseline measurement week, observed counts are [40, 46, 18, 23]. Find the relative frequency for category 2 and state its meaning.

A. 0.46; always divide a count by 100.
B. 46; relative frequency is reported as the original count.
C. 0.362; about 36.2% of the observed units are in category 2.
D. 2.761; divide the total by the category count.

Answer: C

The total is 127. Category 2 has relative frequency 46127=0.362, so 36.2% of the observed ballots were in category 2.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.362; about 36.2% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It does not match the requested calculation. The correct comparison or result is: 0.362; about 36.2% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.
Choice D: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.362; about 36.2% of the observed units are in category 2. Key check: Relative frequency equals category frequency divided by the total count.

Question 35. Frequency and Relative Frequency Tables

For four categories of recovery time at a wildlife clinic in Riverbend during a school-year data collection, observed counts are [58, 32, 21, 55]. Find the relative frequency for category 3 and state its meaning.

A. 21; relative frequency is reported as the original count.
B. 7.905; divide the total by the category count.
C. 0.21; always divide a count by 100.
D. 0.127; about 12.7% of the observed units are in category 3.

Answer: D

The total is 166. Category 3 has relative frequency 21166=0.127, so 12.7% of the observed animals were in category 3.

Why the other choices fail

Choice A: It does not match the requested calculation. The correct comparison or result is: 0.127; about 12.7% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.127; about 12.7% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.127; about 12.7% of the observed units are in category 3. Key check: Relative frequency equals category frequency divided by the total count.

Question 36. Frequency and Relative Frequency Tables

For four categories of checkout time at a grocery cooperative in Midwest consortium during a six-week field trial, observed counts are [50, 65, 29, 56]. Find the relative frequency for category 1 and state its meaning.

A. 0.5; always divide a count by 100.
B. 4; divide the total by the category count.
C. 50; relative frequency is reported as the original count.
D. 0.25; about 25.0% of the observed units are in category 1.

Answer: D

The total is 200. Category 1 has relative frequency 50200=0.25, so 25.0% of the observed customers were in category 1.

Why the other choices fail

Choice A: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.25; about 25.0% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice B: It uses the wrong denominator or omits a required scale adjustment. The correct comparison or result is: 0.25; about 25.0% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.
Choice C: It does not match the requested calculation. The correct comparison or result is: 0.25; about 25.0% of the observed units are in category 1. Key check: Relative frequency equals category frequency divided by the total count.

Frequency and Relative Frequency Tables free-response practice

10-point analytic study rubric used for the sets below
Evidence	Points
Correct target, notation, direction, or group order	2
Correct method/model and defensible conditions	2
Correct setup and execution	3
Contextual interpretation and scope/limitation	2
Clear communication with units and labels	1

FRQ set 1: Frequency and Relative Frequency Tables

Scenario. For four categories of monthly household use at a municipal water office in Great Lakes during a spring 2027 pilot, observed counts are [31, 51, 23, 31]. Find the relative frequency for category 2 and state its meaning.

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

Model response

The total is 136. Category 2 has relative frequency 51136=0.375, so 37.5% of the observed accounts were in category 2.

FRQ set 2: Frequency and Relative Frequency Tables

Scenario. For four categories of weekly material weight at a recycling program in Riverbend during a community outreach cycle, observed counts are [63, 45, 51, 56]. Find the relative frequency for category 1 and state its meaning.

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

Model response

The total is 215. Category 1 has relative frequency 63215=0.293, so 29.3% of the observed households were in category 1.

FRQ set 3: Frequency and Relative Frequency Tables

Scenario. For four categories of recovery time at a wildlife clinic in Prairie District during a multiweek validation study, observed counts are [34, 49, 54, 44]. Find the relative frequency for category 4 and state its meaning.

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

Model response

The total is 181. Category 4 has relative frequency 44181=0.243, so 24.3% of the observed animals were in category 4.

FRQ set 4: Frequency and Relative Frequency Tables

Scenario. For four categories of weekly material weight at a recycling program in New England network during a monthly quality review, observed counts are [20, 39, 61, 22]. Find the relative frequency for category 3 and state its meaning.

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

Model response

The total is 142. Category 3 has relative frequency 61142=0.43, so 43.0% of the observed households were in category 3.

FRQ set 5: Frequency and Relative Frequency Tables

Scenario. For four categories of course completion at a community college in Midwest consortium during a spring 2027 pilot, observed counts are [25, 57, 50, 36]. Find the relative frequency for category 1 and state its meaning.

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

Model response

The total is 168. Category 1 has relative frequency 25168=0.149, so 14.9% of the observed enrolled learners were in category 1.

FRQ set 6: Frequency and Relative Frequency Tables

Scenario. For four categories of response time at a municipal emergency dispatch center in Mountain Region during a summer implementation review, observed counts are [45, 51, 43, 20]. Find the relative frequency for category 3 and state its meaning.

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

Model response

The total is 159. Category 3 has relative frequency 43159=0.27, so 27.0% of the observed calls were in category 3.

FRQ set 7: Frequency and Relative Frequency Tables

Scenario. For four categories of weekly material weight at a recycling program in Lakeside district during a quarterly performance study, observed counts are [42, 22, 62, 19]. Find the relative frequency for category 4 and state its meaning.

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

Model response

The total is 145. Category 4 has relative frequency 19145=0.131, so 13.1% of the observed households were in category 4.

FRQ set 8: Frequency and Relative Frequency Tables

Scenario. For four categories of security wait time at a regional airport authority in Capital Region during a fall 2026 audit, observed counts are [58, 43, 58, 46]. Find the relative frequency for category 3 and state its meaning.

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

Model response

The total is 205. Category 3 has relative frequency 58205=0.283, so 28.3% of the observed travelers were in category 3.

FRQ set 9: Frequency and Relative Frequency Tables

Scenario. For four categories of ballot-processing time at a county election office in Great Lakes during a summer implementation review, observed counts are [18, 53, 57, 50]. Find the relative frequency for category 2 and state its meaning.

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

Model response

The total is 178. Category 2 has relative frequency 53178=0.298, so 29.8% of the observed ballots were in category 2.

FRQ set 10: Frequency and Relative Frequency Tables

Scenario. For four categories of appointment completion at a regional hospital in Pine Ridge during a follow-up evaluation period, observed counts are [23, 64, 22, 23]. Find the relative frequency for category 3 and state its meaning.

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

Model response

The total is 132. Category 3 has relative frequency 22132=0.167, so 16.7% of the observed patients were in category 3.

FRQ set 11: Frequency and Relative Frequency Tables

Scenario. For four categories of part diameter at a regional manufacturer in North Valley during a winter readiness review, observed counts are [31, 41, 30, 63]. Find the relative frequency for category 1 and state its meaning.

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

Model response

The total is 165. Category 1 has relative frequency 31165=0.188, so 18.8% of the observed parts were in category 1.

FRQ set 12: Frequency and Relative Frequency Tables

Scenario. For four categories of application processing time at a housing authority in Cedar Grove during a two-month observation window, observed counts are [43, 43, 19, 32]. Find the relative frequency for category 4 and state its meaning.

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

Model response

The total is 137. Category 4 has relative frequency 32137=0.234, so 23.4% of the observed applications were in category 4.

FRQ set 13: Frequency and Relative Frequency Tables

Scenario. For four categories of lesson completion at a digital learning platform in Mountain Region during a baseline measurement week, observed counts are [61, 35, 46, 23]. Find the relative frequency for category 2 and state its meaning.

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

Model response

The total is 165. Category 2 has relative frequency 35165=0.212, so 21.2% of the observed learners were in category 2.

FRQ set 14: Frequency and Relative Frequency Tables

Scenario. For four categories of ballot-processing time at a county election office in Metro East during a community outreach cycle, observed counts are [31, 64, 42, 58]. Find the relative frequency for category 1 and state its meaning.

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

Model response

The total is 195. Category 1 has relative frequency 31195=0.159, so 15.9% of the observed ballots were in category 1.