AP Stats 1.2: Variables

Observational units and variables

Topic 1.2 gives you the language for describing data before you graph or summarize it: an observational unit is the item or individual you collect a datum from, and a variable is a characteristic that may change from one observational unit to another. In a study of students, each student is an observational unit, and their height, grade level, and favorite subject are variables. Sorting a study into its units and variables is the first move on almost every free-response question, because the rest of the analysis depends on it. Data can take many forms, since numerical and categorical variables, including photographs, sounds, videos, and text, all carry meaningful information.

Categorical vs quantitative variables

Every variable is either categorical or quantitative, and telling them apart decides which graphs and summaries are valid.

• A categorical variable, also called qualitative, takes values that are category names or group labels, such as eye color or brand of phone.
• A quantitative variable, also called numerical, takes numerical values for a measured or counted quantity and generally has units of measure, such as height in centimeters or number of siblings.

A quick test: if averaging the values would make sense, the variable is quantitative. Zip codes look numerical but act as labels, so they are categorical. See qualitative vs quantitative data for more borderline cases.

Discrete vs continuous, parameter vs statistic

Quantitative variables split further. A discrete variable takes on a countable number of values, which may be finite or countably infinite like the whole numbers; the number of pets in a home is discrete. A continuous variable takes on an infinite number of values within an interval and can equal any value between any pair of values, so it is measurable but not countable; a runner's exact time is continuous. Discrete data often come from counting and continuous data from measuring, which is a fast way to tell them apart.

A summary number is named for where it comes from. A parameter is a numerical summary of the variable of interest for a population, and a statistic is a numerical summary for a sample. A statistic usually differs from the unknown parameter but gives you the basis for inference about it, which is the engine of later units. Keep them straight with parameter vs statistic.