Many applications of statistics involve categorical variables, such as gender (male/female), opinion (yes/no/undecided), home ownership (yes/no), or blood type. One common statistical application is to look for relationships between two categorical variables.

Solve the following problems about variables in two-way tables.

## Sample questions

Which of the following variables is categorical?

A. gender

B. hair color

C. zip code

D. Choices (A) and (B)

E. Choices (A), (B), and (C)

**Answer: E.**Choices (A), (B), and (C) (gender; hair color; zip code)Gender, hair color, and zip code are all categorical because the data takes on values that have no numeric meaning. Although zip codes are written with numeric symbols (for example, 10024), the digits are symbols rather than numbers that can be added, subtracted, and so forth.

Which of the following variables would be suitable for a two-way table?

A. years of education

B. height in centimeters

C. homeownership (yes/no)

D. gender

E. Choices (C) and (D)

**Answer: E.**Choices (C) and (D) (homeownership [yes/no]; gender)For a two-way table, the data must be categorical. Years of education and height are numerical in which the numeric values have meaning. Gender and homeownership are categorical and can be used in a two-way table.

For a two-way table including education as one of the variables, which of the following would be an appropriate way to categorize the data?

A. whether someone is a high-school graduate

B. whether someone is a college graduate

C. highest level of school completed

D. Choices (A) and (B)

E. Choices (A), (B), and (C)

**Answer: E.**Choices (A), (B), and (C) (whether someone is a high-school graduate; whether someone is a college graduate; highest level of school completed)*Whether someone is a high-school graduate*and*whether someone is a college graduate*both clearly have only two possible values — yes or no — and can be considered appropriate for a two-way table.*Highest level of school completed*is also a categorical variable whose possible values can be listed (for example, "less than high school," "high-school graduate," "some college," "college graduate," and "graduate school"). Therefore, it's also appropriate for a two-way table.

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