AP Statistics Quiz: Representing A Categorical Variable With Tables
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Representing A Categorical Variable With TablesQuestion 1 of 20

A researcher collects data on the preferred type of movie from a sample of moviegoers. The categories are Action, Comedy, Drama, and Sci-Fi. Which of the following is NOT information that can be obtained from a frequency table of this data?

The total number of moviegoers in the sample.
The average rating moviegoers gave for their preferred movie type.
The number of moviegoers who prefer Comedy.
The movie type that was most frequently preferred.
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AP Statistics Quiz

AP Statistics Quiz: Representing A Categorical Variable With Tables

Practice Representing A Categorical Variable With Tables in AP Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Representing A Categorical Variable With Tables, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A researcher collects data on the preferred type of movie from a sample of moviegoers. The categories are Action, Comedy, Drama, and Sci-Fi. Which of the following is NOT information that can be obtained from a frequency table of this data?

  1. The total number of moviegoers in the sample.
  2. The average rating moviegoers gave for their preferred movie type. (correct answer)
  3. The number of moviegoers who prefer Comedy.
  4. The movie type that was most frequently preferred.
Explanation: A frequency table for a categorical variable like 'preferred movie type' can show counts for each category, the total count, and the most frequent category (the mode). It cannot provide information about a quantitative variable like an 'average rating,' as that data is not part of the categorical frequency count.

Question 2

A library tracks the genres of books checked out by patrons. A relative frequency table shows the following: Fiction: 0.52, Non-Fiction: 0.28, Young Adult: 0.15. The rest are Children's books. If 400 books were checked out in total, what is the frequency of Children's books?

  1. 20 (correct answer)
  2. 5
  3. 95
  4. 380
Explanation: First, find the relative frequency of Children's books. The sum of relative frequencies must be 1. 1−(0.52+0.28+0.15)=1−0.95=0.051 - (0.52 + 0.28 + 0.15) = 1 - 0.95 = 0.05. Then, find the frequency by multiplying this relative frequency by the total number of books: 0.05×400=200.05 \times 400 = 20.

Question 3

An environmental agency tested 150 rivers and classified their pollution level as Low, Medium, or High. They found 63 rivers had a Low pollution level and 45 had a Medium pollution level.

Which of the following represents the relative frequency table for the pollution levels of the 150 rivers?

  1. Low: 0.42, Medium: 0.30, High: 0.28 (correct answer)
  2. Low: 63, Medium: 45, High: 42
  3. Low: 0.28, Medium: 0.30, High: 0.42
  4. Low: 0.63, Medium: 0.45, High: 0.42
Explanation: First, find the frequency for High: 150−63−45=42150 - 63 - 45 = 42. Then, calculate relative frequencies: Low is 63/150=0.4263/150 = 0.42, Medium is 45/150=0.3045/150 = 0.30, and High is 42/150=0.2842/150 = 0.28. Choice A correctly lists these relative frequencies. Choice B lists frequencies. Choices C and D use incorrect calculations.

Question 4

A survey of 300 commuters in a large city asked for their primary mode of transport. A frequency table of the results is shown below: Car: 165 Bus: 75 Subway: 45 Walk/Bike: 15

A city planner claims that cars are the primary mode of transport for a majority of commuters. Which of the following statements correctly evaluates this claim using the provided data?

  1. The claim is correct because the frequency for Car (165) is the highest among all categories.
  2. The claim is correct because the relative frequency for Car is 0.55, which is greater than 0.50. (correct answer)
  3. The claim is incorrect because 135 commuters use a mode of transport other than a car.
  4. The claim is incorrect because the frequency for Car (165) is not more than twice the next highest frequency (75).
Explanation: The term 'majority' means more than 50%. To evaluate this, we need the relative frequency. The relative frequency for Car is 165/300=0.55165/300 = 0.55. Since 0.55>0.500.55 > 0.50, the claim is supported by the data. While choice A is true (Car is the mode), it doesn't directly address the 'majority' claim. Choices C and D use flawed reasoning to evaluate the claim.

Question 5

A fitness center manager is researching which class type members most want added to the schedule. From the population of current members, a random sample of 160 members is surveyed and each member selects a preferred new class type (a categorical variable). The distribution is shown below.

Which statement is supported by the data?

Preferred new class typeFrequencyRelative frequency
Yoga520.325
Strength training440.275
Cycling360.225
Dance280.175
  1. Strength training is preferred by about 44% of surveyed members.
  2. Cycling is the most preferred new class type in the sample.
  3. Yoga is preferred by the largest proportion of surveyed members, about 32.5%. (correct answer)
  4. Dance is preferred by 28% of surveyed members.
  5. More than half of surveyed members preferred cycling or dance.
Explanation: The skill assessed is representing a categorical variable with tables, using frequency and relative frequency to evaluate preferred new class types among 160 members. Choice C is supported by yoga's relative frequency of 0.325, or 32.5%, the largest proportion, greater than strength training at 27.5%. Evidence includes 52/160 = 0.325, confirming its lead. A common distractor is choice A, claiming strength training at about 44%, but that's the frequency, not the 27.5% relative. Choice D similarly mistakes dance's frequency 28 for 28%. A transferable lesson for categorical tables is to distinguish frequencies from relative frequencies when making proportion-based claims, and verify modes by comparing decimals or percentages directly.

Question 6

A city transportation office is studying commuting habits of adults who live within city limits. A random sample of 200 adults is asked to report their primary commute mode (a categorical variable). The distribution is shown below.

Which statement is supported by the data?

Primary commute modeFrequencyRelative frequency
Drive alone980.490
Carpool340.170
Public transit460.230
Bike/Walk220.110
  1. Public transit is the most common commute mode in the sample.
  2. Fewer than one-fourth of sampled adults reported public transit as their primary mode.
  3. About 49% of sampled adults reported driving alone, which is the largest category. (correct answer)
  4. Carpool and bike/walk together account for more than half of the sample.
  5. The frequency for bike/walk is 0.110 adults.
Explanation: The skill tested here involves representing a categorical variable with tables, focusing on interpreting frequencies and relative frequencies for commute modes in a sample of 200 adults. Choice C is supported as the relative frequency for driving alone is 0.490, or about 49%, and it is the largest category, exceeding public transit at 23% and others. This is evidenced by the frequency of 98, which is 98/200 = 0.49, confirming it's the mode. A frequent distractor is choice E, claiming the frequency for bike/walk is 0.110 adults, but 0.110 is the relative frequency, while the actual frequency is 22, mixing up the two columns. Choice D incorrectly adds carpool and bike/walk to over half (0.170 + 0.110 = 0.280), which is less than 0.5. A transferable mini-lesson for categorical tables is to always verify proportions by dividing frequencies by the total and compare them to assess dominance or combinations, avoiding assumptions about aggregates without calculation.

Question 7

A school counselor wants to understand how 9th-grade students at Central High prefer to receive academic support. The counselor surveys a random sample of 120 ninth graders and records each student's preferred support method (a categorical variable). Results are summarized below.

Which statement is supported by the data in the table?

Preferred support methodFrequencyRelative frequency
One-on-one tutoring420.350
Small-group sessions300.250
Online resources240.200
Teacher office hours180.150
Peer mentoring60.050
  1. More students preferred small-group sessions than online resources.
  2. About 35%35\% of surveyed students preferred one-on-one tutoring, the highest proportion. (correct answer)
  3. Teacher office hours were preferred by about 18% of surveyed students.
  4. Peer mentoring was preferred by about 6% of surveyed students.
  5. A majority of surveyed students preferred either online resources or teacher office hours.
Explanation: This question assesses the skill of representing a categorical variable with tables by interpreting frequency and relative frequency to identify supported statements about students' preferred academic support methods. The data supports choice B because the relative frequency for one-on-one tutoring is 0.3500.350, or 35%35\%, which is indeed the highest proportion among the options, as confirmed by comparing it to 0.2500.250, 0.2000.200, 0.1500.150, and 0.0500.050. Evidence from the table shows 42 students chose this out of 120, yielding exactly 35%35\%, outperforming others like small-group sessions at 25%25\%. A common distractor is choice C, which claims about 18% preferred teacher office hours, but the actual relative frequency is 0.1500.150 or 15%, likely confusing the frequency count of 18 with a percentage. Another distractor, choice D, states about 6% for peer mentoring, but it's precisely 5%, highlighting the need for accurate reading. In interpreting categorical tables, a key lesson is to use relative frequencies for proportions and compare them directly to identify modes or rankings, ensuring calculations align with the total sample size for validity.

Question 8

A table reports athletes 80, musicians 50, neither 30, for 120 students. Counts sum to 160. The table is invalid because...

  1. Counts should be percents
  2. The categories overlap (correct answer)
  3. Categories should be sorted
  4. Relative tables fix this
Explanation: The categories are not mutually exclusive: a student can be both an athlete and a musician, so the counts double-count those students. That is why 80 + 50 + 30 exceeds 120. The tempting wrong answer is that counts should be percents, but percents would not fix double-counting from overlapping categories.

Question 9

Class X: 10 of 25 prefer A. Class Y: 10 of 100 prefer A. A frequency table shows 10 votes each. Why is it misleading?

  1. Relative frequencies exceed 1
  2. Counts are always too small
  3. Same count, different rates (correct answer)
  4. Totals cannot be computed here
Explanation: In Class X, 10 out of 25 means 40% prefer A, while in Class Y, 10 out of 100 means only 10%, so equal counts hide very different rates. The tempting mistake is treating the equal vote totals as comparable without considering each class size.

Question 10

A survey of 1,200 residents: 480 rent, 360 own, 240 other. A table says rent 0.40, own 0.30, other 0.30. What is wrong?

  1. Other should be 0.20, not 0.30 (correct answer)
  2. Own should be 0.45, not 0.30
  3. Rent should be 0.48, not 0.40
  4. Total is 1.00, so it is valid
Explanation: Among 1,200 residents, each proportion is count divided by 1,200: rent 480/1,200 = 0.40, own 360/1,200 = 0.30, other 240/1,200 = 0.20. So the table's 0.30 for other is wrong. The tempting mistake is thinking rent is 0.48, which comes from dividing 480 by 1,000 instead of 1,200.

Question 11

A table with three categories gives 26%, 38%, 39%; each was rounded to nearest percent. Their sum is 103%. What is true?

  1. Normalizing by 103 fixes it
  2. Rounding explains the total
  3. The table is valid as shown
  4. Rounded values sum too high (correct answer)
Explanation: Each rounded value can be off by no more than half a percentage point, so three rounded values can deviate from 100 by at most 1.5 points, putting the total between 98.5 and 101.5. A sum of 103 is outside that range, so the rounded values sum too high. You might be tempted to rescale by 103, but that only forces a new total of 100 instead of explaining why the original rounded entries are inconsistent.

Question 12

Car 52%, bus 23%, bike 18%, walk 7%. A cumulative table gives 52, 75, 93, 100. The main flaw is that...

  1. Category order is arbitrary (correct answer)
  2. It should use raw counts here
  3. Order should be by frequency
  4. The last entry should be 1.00
Explanation: A cumulative table only makes sense when the categories have a meaningful order; car, bus, bike, and walk do not, so their sequence is arbitrary and the cumulative totals are meaningless. The last entry of 100 is fine because the table uses percentages, not decimal proportions. The tempting wrong answer is that the last entry should be 1.00, but that only applies if the table used decimals like 0.52 instead of 52.

Question 13

A community health clinic is studying how patients prefer to be reminded about appointments. From the population of patients who had an appointment last month, a random sample of 110 patients is surveyed and each chooses a preferred reminder method (a categorical variable). The distribution is shown below.

Which statement is supported by the data?

Preferred reminder methodFrequencyRelative frequency
Text message550.500
Phone call220.200
Email270.245
No reminder60.055
  1. Email is preferred by more patients than phone calls in the sample. (correct answer)
  2. Text messages are preferred by about 55% of the sampled patients.
  3. No reminder is preferred by about 6% of the sampled patients.
  4. Phone calls are preferred by about 22.0% of the sampled patients.
  5. A majority of the sampled patients preferred either email or phone calls.
Explanation: The skill here involves representing a categorical variable with tables by analyzing frequency and relative frequency for preferred reminder methods in 110 patients. Choice A is supported because email has a frequency of 27, exceeding phone calls at 22, indicating more patients prefer email. Evidence from the table confirms 27 > 22, directly comparing counts. A common distractor is choice B, claiming text messages at about 55%, but it's 0.500 or 50%, an overestimation. Choice D says phone calls at about 22.0%, mistaking frequency for relative frequency (20%). A mini-lesson on categorical tables is to compare frequencies for count-based claims and relative frequencies for proportions, calculating totals or sums to validate statements about majorities or preferences.

Question 14

A technology teacher wants to summarize which device students most often use to complete homework. A random sample of 90 students in the school is selected, and each student reports the primary device used (a categorical variable). The distribution is shown below.

Which statement is supported by the data?

Primary homework deviceFrequencyRelative frequency
Laptop390.433
Tablet180.200
Phone240.267
Desktop90.100
  1. Phones are used by the largest proportion of students in the sample.
  2. Tablets are used by about 18% of students in the sample.
  3. Laptops are the most common primary device in the sample, at about 43.3%. (correct answer)
  4. Desktops and tablets together account for about 63.3% of the sample.
  5. The frequency for phone is 0.267 students.
Explanation: This problem focuses on the skill of representing a categorical variable with tables, interpreting frequency and relative frequency for primary homework devices in 90 students. Choice C is supported, with laptops at 0.433 or about 43.3%, the most common, surpassing phones at 26.7%. This is backed by 39/90 ≈ 0.433, the highest. A typical distractor is choice E, stating the frequency for phone is 0.267 students, confusing relative frequency with the actual count of 24. Choice D wrongly adds desktops and tablets to 63.3%, but it's 30%. For interpreting categorical tables, use relative frequencies to assess prevalence and add them for combinations, ensuring you reference the correct column to avoid mixing counts and proportions.

Question 15

A marketing team is studying which social media platform customers most associate with a brand. From the population of customers who follow the brand online, a random sample of 140 customers is surveyed, and each customer selects the platform they most associate with the brand (a categorical variable). The distribution is shown below.

Which statement is supported by the data?

Platform most associated with the brandFrequencyRelative frequency
Instagram560.400
TikTok420.300
YouTube280.200
Facebook140.100
  1. TikTok is the least common platform in the sample.
  2. Instagram is the most common platform in the sample, with 56 respondents (40%). (correct answer)
  3. YouTube is associated with the brand by about 28% of respondents.
  4. Facebook and YouTube together account for about 10% of respondents.
  5. More respondents selected Facebook than YouTube.
Explanation: The skill evaluated is representing a categorical variable with tables, interpreting frequency and relative frequency for social media platforms associated with a brand in 140 customers. Choice B is supported, with Instagram at 56 respondents and 0.400 or 40%, the most common. Evidence includes 56/140 = 0.4, outperforming others. A key distractor is choice C, claiming YouTube at about 28%, but 28 is frequency, not the 20% relative. Choice D errs by adding Facebook and YouTube to 10%, when it's 30%. A transferable mini-lesson for categorical tables is to use frequencies for counts and relative frequencies for percentages, verifying combinations by summing proportions to check aggregate claims accurately.

Question 16

An environmental club wants to describe recycling behavior among students at a high school. A random sample of 100 students is asked how often they recycle at home (a categorical variable). The results are shown below.

Which statement is supported by the data?

Recycling frequencyFrequencyRelative frequency
Always280.280
Often340.340
Sometimes260.260
Never120.120
  1. Always is the most common response in the sample.
  2. Often is the most common response in the sample, at about 34%. (correct answer)
  3. Sometimes and never together account for about 88% of the sample.
  4. The frequency for never is 0.120 students.
  5. More students responded always than often.
Explanation: This question targets the skill of representing a categorical variable with tables by examining frequency and relative frequency for recycling behaviors in 100 students. The statement in choice B is supported, as often has 0.340 or about 34%, the highest relative frequency, exceeding always at 28%. This is evidenced by 34/100 = 0.34, making it the mode. A key distractor is choice D, which states the frequency for never is 0.120 students, but 0.120 is the relative frequency, while frequency is 12. Choice A incorrectly identifies always as most common, ignoring the higher count for often. In working with categorical tables, always calculate and compare relative frequencies to spot the dominant category, and combine them for aggregate claims to avoid errors in interpretation.

Question 17

A university dining services team is researching beverage choices among students who eat lunch on campus. A random sample of 150 students is asked to choose their most common lunch beverage (a categorical variable). The results are summarized below.

Which statement is supported by the data?

Lunch beverageFrequencyRelative frequency
Water630.420
Soda360.240
Coffee/Tea300.200
Juice210.140
  1. Juice is chosen by about 21% of the sampled students.
  2. Soda is chosen by fewer students than coffee/tea.
  3. Water is the most common beverage in the sample, at about 42%. (correct answer)
  4. More than half of sampled students chose soda or juice.
  5. The relative frequency for coffee/tea is 30.
Explanation: This problem evaluates the ability to represent a categorical variable with tables by analyzing frequency and relative frequency for lunch beverage choices among 150 students. The data supports choice C since water has a relative frequency of 0.420, or 42%, and it's the highest, surpassing soda at 24%. Supporting evidence includes the frequency of 63, where 63/150 = 0.42, clearly the mode. A typical distractor is choice A, stating juice is about 21%, but 0.140 is 14%, possibly mistaking the frequency 21 for a percentage. Choice E errs by saying the relative frequency for coffee/tea is 30, confusing it with the frequency count. For interpreting categorical tables, remember to differentiate counts from proportions and use relative frequencies to determine popularity, calculating sums for combined categories to check claims like majorities.

Question 18

A school district is researching which after-school activity middle school students participate in most. A random sample of 125 middle school students is selected, and each student reports their primary after-school activity (a categorical variable). Results are shown below.

Which statement is supported by the data?

Primary after-school activityFrequencyRelative frequency
Sports500.400
Clubs310.248
Part-time job190.152
Homework/Study250.200
  1. Clubs account for about 31% of the students in the sample.
  2. Sports are the most common primary activity in the sample, at about 40%. (correct answer)
  3. Homework/study is the least common primary activity in the sample.
  4. More students reported part‑time job than homework/study.
  5. Sports and clubs together account for fewer than half of the sample.
Explanation: This question tests representing a categorical variable with tables, using frequency and relative frequency for after-school activities in 125 students. Choice B is supported as sports has 0.400 or 40%, the most common, higher than clubs at 24.8%. This is evidenced by 50/125 = 0.4, the mode. A frequent distractor is choice A, stating clubs at about 31%, but 31 is the frequency, not the 24.8% relative. Choice C incorrectly calls homework the least, despite it exceeding part-time jobs. In interpreting categorical tables, identify the highest relative frequency for the most common category and compare counts carefully for rankings, avoiding confusion between absolute and proportional values.

Question 19

A public library is evaluating how adult patrons prefer to access books. From the population of adult patrons who used the library this month, the library selects a random sample of 80 patrons and records each patron's preferred format (a categorical variable). The distribution is shown below.

Which statement is supported by the data?

Preferred book formatFrequencyRelative frequency
Print440.550
E-book200.250
Audiobook120.150
Other40.050
  1. E-books are preferred by a majority of the sampled patrons.
  2. Audiobooks are preferred by about 12% of the sampled patrons.
  3. Print is the least common preferred format in the sample.
  4. Print is the most common preferred format in the sample, at about 55%. (correct answer)
  5. Other formats account for 4% of the sampled patrons.
Explanation: The skill here is representing a categorical variable with tables, interpreting frequency and relative frequency for preferred book formats in a sample of 80 patrons. Choice D is backed by the data, with print at 0.550 or 55%, the highest proportion, outranking e-books at 25%. Evidence comes from 44/80 = 0.55, establishing it as the most common. A common distractor is choice B, claiming audiobooks at about 12%, but it's 0.150 or 15%, likely a misreading of the table. Choice E says other at 4%, but it's 0.050 or 5%, a slight but incorrect approximation. A useful mini-lesson on categorical tables is to rely on relative frequencies for percentage claims and compare them to identify the least or most preferred options, ensuring approximations align closely with exact values.

Question 20

A dataset contains observations on the eye color of 80 individuals. If a frequency table is created for this data, which of the following must be true?

  1. The sum of the frequencies will be equal to the number of distinct eye colors.
  2. Each frequency must be less than the corresponding relative frequency.
  3. The sum of the frequencies will be equal to 80. (correct answer)
  4. The category with the highest frequency will have a relative frequency of 1.0.
Explanation: The sum of the frequencies (counts) in a frequency table must equal the total number of observations in the dataset, which is 80 in this case. The other statements are incorrect definitions or properties of frequency tables.