## What are Variables?

In statistics, a variable has two defining characteristics:

- A variable is an attribute that describes a place, idea or thing
- The value of the variable can “vary” from one entity to another

For example, a person’s height is a potential variable, which could have the value of “tall” for one person and “short” for another.

**Qualitative vs. Quantitative Variables**

Variables can be classified as Qualitative (categorical) or Quantitative (numerical):

- Categorical: Categorical variables take on values that are names or labels. The colour of eyes (e.g. black, blue) would be an example of categorical variable.
- Numerical: Quantitative variables are numerical and represent a measurable quantity. For example, when we speak of the height of students, we are talking about the height (in inches or feet) of the students – a measurable attribute. Therefore, height 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 its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable. The following examples will clarify the difference between discrete and continuous 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 2.3 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.