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.

Relative frequency is calculated by taking the count (frequency) for a specific category and dividing it by the total sample size (total number of observations). The other options misstate this fundamental relationship.

First, find the relative frequency of Children's books. The sum of relative frequencies must be 1. $$1 - (0.52 + 0.28 + 0.15) = 1 - 0.95 = 0.05$$. Then, find the frequency by multiplying this relative frequency by the total number of books: $$0.05 \times 400 = 20$$.

First, find the frequency for High: $$150 - 63 - 45 = 42$$. Then, calculate relative frequencies: Low is $$63/150 = 0.42$$, Medium is $$45/150 = 0.30$$, and High is $$42/150 = 0.28$$. Choice A correctly lists these relative frequencies. Choice B lists frequencies. Choices C and D use incorrect calculations.

A relative frequency of 0.25 means that the category accounts for $$1/4$$, or one-quarter, of the total observations. Without knowing the total number of albums sold, we cannot determine the exact frequency (count), so A and D are not necessarily true. We also cannot determine if Rock was the most popular genre, as another genre could have a relative frequency greater than 0.25.

The term 'majority' means more than 50%. To evaluate this, we need the relative frequency. The relative frequency for Car is $$165/300 = 0.55$$. Since $$0.55 > 0.50$$, 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.

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.

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.

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.

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.