AP* Statistics Tutorial: Variables

A variable is a symbol (e.g., x, Y, or σ) that represents any of a specified set of values.

For example, suppose we let the variable x represent the percentage of defective units in a shipment of widgets. Since x is a percentage, the variable x could take on any value between 0 and 100.

Categorical vs. Quantitative Variables

Variables can be classified as categorical (aka, qualitative) or quantitative (aka, numerical).

• Categorical. Categorical variables take on values that are names or labels. The color of a ball (e.g., red, green, blue) or the breed of a dog (e.g., collie, shepherd, terrier) would be examples of categorical variables.
  
  
• Quantitative. Quantitative variables are numerical. They represent a measurable quantity. For example, when we speak of the population of a city, we are talking about the number of people in the city - a measurable attribute of the city. Therefore, population would be a quantitative variable.

Discrete vs. Continuous Variables

Quantitative variables can be further classified as discrete or continuous. If a variable can take on any value between two specified values, it is called a continuous variable; otherwise, it is called a discrete variable.

Some examples will clarify the difference between discrete and continouous variables.

• Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.
  
  
• Suppose we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity. However, it could not be any number between 0 and plus infinity. We could not, for example, get 2.5 heads. Therefore, the number of heads must be a discrete variable.

Univariate vs. Bivariate Data

Statistical data is often classified according to the number of variables being studied.

• Univariate data. When we conduct a study that looks at only one variable, we say that we are working with univariate data. Suppose, for example, that we conducted a survey to estimate the average weight of high school students. Since we are only working with one variable (weight), we would be working with univariate data.
  
  
• Bivariate data. When we conduct a study that examines the relationship between two variables, we are working with bivariate data. Suppose we conducted a study to see if there were a relationship between the height and weight of high school students. Since we are working with two variables (height and weight), we would be working with bivariate data

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