Discrete and Continuous Variables

Fundamentals of Social Statistics by Adam J. McKee

In research studies, variables can be classified based on the types of values they can have. There are two main types: discrete variables, which have distinct categories and can’t be divided further, and continuous variables, which can be broken down into an almost infinite number of smaller parts.

Understanding Discrete Variables

Discrete variables have separate categories that are indivisible. These categories are well-defined, and you can’t break them down into smaller parts. Let’s use the example of blood type to understand this better. Blood types are generally categorized as A, B, AB, or O. You can’t be “half-A” or “one-third B”; you belong to one category or the other.

Another way to look at discrete variables is by considering them as counts of things. For example, consider the variable of felony convictions. You could have zero convictions, one conviction, two convictions, and so on. What you can’t have is a fraction of a conviction like 2.78 felonies. The values are whole numbers, and they represent countable, distinct categories.

Exploring Continuous Variables

Continuous variables are the opposite of discrete variables. They can be divided into an infinite number of smaller parts. Think of annual household income as an example. It’s measured in dollars and cents, allowing for a broad range of specific values. You could make $50,000 a year, or $50,000.01, or $50,000.02, and so on.

Continuous variables can be visualized along a line, much like a number line in math. There are no clear breaks or divisions along this line. For instance, household income could range from zero to millions of dollars, falling anywhere along that line.

It’s also worth noting that it’s rare for two subjects to have the same exact value for a continuous variable. Even if two households earn $50,000 a year, when you add cents to the equation, the chances of them earning the exact same amount down to the last cent are extremely low.

Why the Difference Matters

Understanding whether a variable is discrete or continuous is crucial for data analysis. Different types of variables require different statistical methods. For example, a discrete variable may be analyzed using frequency counts, while a continuous variable may require more complex calculations like averages or standard deviations.

Additionally, the type of variable affects how the data is presented. Discrete variables are often shown in bar graphs, while continuous variables are usually displayed using line graphs or histograms.

Summary

In research, variables can be either discrete or continuous, depending on the types of values they can hold. Discrete variables have indivisible categories and are often whole, countable numbers. Continuous variables can be broken down into an almost infinite number of smaller parts and usually fall along a continuous line. Knowing the difference between these two types of variables is essential for accurately analyzing and presenting data.


Key Terms

Variable, Constant, Continuous, Discrete, Experimental Group, Control Group, Independent Variable, Dependent Variable, Environmental Variable, Data, Attribute (of a Variable), Level (of a Variable)


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Last Modified:  09/11/2023

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