Which of the following questions can be answered by using a two-way table?

• A. What is the $\mathrm{standard\; deviation}$ of test scores in a sample?
• B. Is there an association between gender and preferred type of movie in a group of people?
• C. What is the $\mathrm{mean}$ height of students in a class?
• D. How does the $\mathrm{median}$ income of a city compare to the $\mathrm{national\; average}$?

Answer: (B)

Verified step by step guidance

1. Understand what a two-way table (also called a contingency table) is: it is a table that displays the frequency counts of two categorical variables simultaneously, allowing us to examine the relationship or association between these two variables.
2. Identify the type of data involved in each question: standard deviation and mean height involve numerical data, while gender and preferred type of movie are categorical variables.
3. Recognize that a two-way table is appropriate when you want to analyze the association between two categorical variables, such as gender (male/female) and preferred movie type (e.g., action, comedy, drama).
4. Note that questions about standard deviation, mean, or median involve numerical summaries and are not answered using two-way tables, but rather with numerical descriptive statistics or comparisons.
5. Conclude that the question 'Is there an association between gender and preferred type of movie in a group of people?' can be answered using a two-way table because it involves two categorical variables and their relationship.