Representing a Categorical Variable with Tables
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AP Statistics › Representing a Categorical Variable with Tables
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 type | Frequency | Relative frequency |
|---|---|---|
| Yoga | 52 | 0.325 |
| Strength training | 44 | 0.275 |
| Cycling | 36 | 0.225 |
| Dance | 28 | 0.175 |

Cycling is the most preferred new class type in the sample.
Strength training is preferred by about 44% of surveyed members.
Yoga is preferred by the largest proportion of surveyed members, about 32.5%.
More than half of surveyed members preferred cycling or dance.
Dance is preferred by 28% of surveyed members.
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.
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 mode | Frequency | Relative frequency |
|---|---|---|
| Drive alone | 98 | 0.490 |
| Carpool | 34 | 0.170 |
| Public transit | 46 | 0.230 |
| Bike/Walk | 22 | 0.110 |

About 49% of sampled adults reported driving alone, which is the largest category.
Carpool and bike/walk together account for more than half of the sample.
The frequency for bike/walk is 0.110 adults.
Public transit is the most common commute mode in the sample.
Fewer than one-fourth of sampled adults reported public transit as their primary mode.
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.
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 method | Frequency | Relative frequency |
|---|---|---|
| One-on-one tutoring | 42 | 0.350 |
| Small-group sessions | 30 | 0.250 |
| Online resources | 24 | 0.200 |
| Teacher office hours | 18 | 0.150 |
| Peer mentoring | 6 | 0.050 |
Peer mentoring was preferred by about 6% of surveyed students.
More students preferred small-group sessions than online resources.
A majority of surveyed students preferred either online resources or teacher office hours.
Teacher office hours were preferred by about 18% of surveyed students.
About $35%$ of surveyed students preferred one-on-one tutoring, the highest proportion.
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 $0.350$, or $35%$, which is indeed the highest proportion among the options, as confirmed by comparing it to $0.250$, $0.200$, $0.150$, and $0.050$. Evidence from the table shows 42 students chose this out of 120, yielding exactly $35%$, outperforming others like small-group sessions at $25%$. A common distractor is choice C, which claims about 18% preferred teacher office hours, but the actual relative frequency is $0.150$ 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.
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 method | Frequency | Relative frequency |
|---|---|---|
| Text message | 55 | 0.500 |
| Phone call | 22 | 0.200 |
| 27 | 0.245 | |
| No reminder | 6 | 0.055 |

A majority of the sampled patients preferred either email or phone calls.
Text messages are preferred by about 55% of the sampled patients.
Email is preferred by more patients than phone calls in the sample.
Phone calls are preferred by about 22.0% of the sampled patients.
No reminder is preferred by about 6% of the sampled patients.
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.
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 device | Frequency | Relative frequency |
|---|---|---|
| Laptop | 39 | 0.433 |
| Tablet | 18 | 0.200 |
| Phone | 24 | 0.267 |
| Desktop | 9 | 0.100 |

Tablets are used by about 18% of students in the sample.
Desktops and tablets together account for about 63.3% of the sample.
Laptops are the most common primary device in the sample, at about 43.3%.
Phones are used by the largest proportion of students in the sample.
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.
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 brand | Frequency | Relative frequency |
|---|---|---|
| 56 | 0.400 | |
| TikTok | 42 | 0.300 |
| YouTube | 28 | 0.200 |
| 14 | 0.100 |

More respondents selected Facebook than YouTube.
Instagram is the most common platform in the sample, with 56 respondents (40%).
TikTok is the least common platform in the sample.
Facebook and YouTube together account for about 10% of respondents.
YouTube is associated with the brand by about 28% of respondents.
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.
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 frequency | Frequency | Relative frequency |
|---|---|---|
| Always | 28 | 0.280 |
| Often | 34 | 0.340 |
| Sometimes | 26 | 0.260 |
| Never | 12 | 0.120 |

More students responded always than often.
The frequency for never is 0.120 students.
Often is the most common response in the sample, at about 34%.
Always is the most common response in the sample.
Sometimes and never together account for about 88% of the sample.
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.
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 beverage | Frequency | Relative frequency |
|---|---|---|
| Water | 63 | 0.420 |
| Soda | 36 | 0.240 |
| Coffee/Tea | 30 | 0.200 |
| Juice | 21 | 0.140 |
Soda is chosen by fewer students than coffee/tea.
Water is the most common beverage in the sample, at about 42%.
More than half of sampled students chose soda or juice.
Juice is chosen by about 21% of the sampled students.
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.
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 activity | Frequency | Relative frequency |
|---|---|---|
| Sports | 50 | 0.400 |
| Clubs | 31 | 0.248 |
| Part-time job | 19 | 0.152 |
| Homework/Study | 25 | 0.200 |

Sports are the most common primary activity in the sample, at about 40%.
More students reported part‑time job than homework/study.
Homework/study is the least common primary activity in the sample.
Clubs account for about 31% of the students in the sample.
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.
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 format | Frequency | Relative frequency |
|---|---|---|
| 44 | 0.550 | |
| E-book | 20 | 0.250 |
| Audiobook | 12 | 0.150 |
| Other | 4 | 0.050 |

E-books are preferred by a majority of the sampled patrons.
Print is the most common preferred format in the sample, at about 55%.
Print is the least common preferred format in the sample.
Other formats account for 4% of the sampled patrons.
Audiobooks are preferred by about 12% 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.