Discrete and continuous are two broad categories of numerical data. Numeric variables represent characteristics that you can express as numbers rather than descriptive language.
When you have a numeric variable, you need to determine whether it is discrete or continuous.
In broad strokes, the critical factor is the following:
- You count discrete data.
- You measure continuous data.
Let’s dig a little deeper into the differences!
Discrete Data
Discrete data can only assume specific values that you cannot subdivide. Typically, you count discrete values, and the results are integers. For example, if you work at an animal shelter, you’ll count the number of cats.
Discrete variables can only take on specific values. For example, you might count 20 cats at the animal shelter. These variables cannot have fractional or decimal values. You can have 20 or 21 cats, but not 20.5! Natural numbers have discrete values.
Other examples of discrete data include:
- The number of books you check out from the library.
- The number of heads in a sequence of coin tosses.
- The result of rolling a die.
- The number of patients in a hospital.
- The population of a country.
While discrete variables have no decimal places, the average of these values can be fractional. For example, families can have only a discrete number of children: 1, 2, 3, etc. However, the average number of children per family can be 2.2.
Frequently, you’ll use bar charts to graph discrete data because the separate bars emphasize the distinct nature of each value. However, it’s appropriate to use other graphs as well.
When you have discrete values of a qualitative nature (i.e., attributes rather than numbers), it’s called categorical or nominal data.
Continuous Data
Continuous data can assume any numeric value and can be meaningfully split into smaller parts. Consequently, they have valid fractional and decimal values. In fact, continuous variables have an infinite number of potential values between any two points. Generally, you measure them using a scale.
When you see decimal places for individual data points, you’re looking at a continuous variable.
For example, you have continuous data when you measure weight, height, length, time, and temperature.
Frequently, you’ll use histograms and scatterplots to graph continuous variables. These graphs are designed to handle values that fall on a continuous spectrum and have decimal places.
Discrete vs. Continuous Variables Summary
| Discrete | Continuous |
| Specific values that you cannot divide. | Infinite number of fractional values between any two values. |
| Counting | Measuring |
Both types are essential in statistics. At the animal shelter, after counting the cats, you’ll weigh them. The counts are discrete values while their weights are continuous. Chances are you’ll need to analyze both types of data.
It’s vital to recognize which types of variables you have because there are different ways to graph and analyze them. To learn more about how to assess different data types, read the following posts:
- Data Types and How to Graph Them
- Comparing Hypothesis Tests by Types of Variables
- Choosing Regression Analysis Based on Data Types
- Probability Distributions for Discrete and Continuous Variables
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