Discrete vs. Continuous Variables: How they differ and Why it Matters?

Discrete vs. Continuous Variables
Discrete vs. Continuous Variables

In statistics, we commonly come across two types of variables, discrete and continuous variables; these two types of data differ in their measurement, making them suitable for various statistical methods.

I believe that understanding the difference between discrete and continuous variables is crucial in the application of statistics and probability in research, finance, social sciences, engineering, and many other fields.

In this blog, I will explore in detail what a discrete variable and a continuous variable are, how they differ, and when to use them. If, like most of my students, you wonder if probability is harder than calculus, I wrote a whole article that I encourage you to read.

What Are Discrete Variables?

Discrete variables are those that can only take a finite or countable number of distinct values, which can be integers or whole numbers, and there are gaps between the values. In other words, discrete data can only be represented using whole numbers and cannot be measured or expressed in decimal points or fractions.

Examples of discrete variables are the following:

  • The number of students in a class.
  • The number of heads in a coin toss.
  • The number of children in a family.
  • The number of cars a person has owned throughout their life.
  • The number of pieces of candy in a bag.

Discrete variables are typically represented visually by bar graphs or histograms, which show the frequency of each value and only take on specific values and cannot be divided into smaller units.

Statisticians and data analysts use histograms, tally charts, bar graphs, line charts, and pie charts to visualize discrete data (Source: The Open University)

Below are a few key characteristics of discrete variables:

  • Countable, finite, and nondivisible: Discrete variables contain finite, numeric, and non-negative integers. 
  • Discrete variables are generally easy to visualize using bar charts, line charts, or pie charts.
  • Discrete variables can be categorical, containing a finite number of data values, including nationality or gender. 

What Are Continuous Variables?

Continuous variables are defined as variables that can take on an infinite number of values within a specified range. Generally, continuous data can be measured and expressed in decimal points or fractions.

Continuous data can be represented on a number line, and each possible value can be associated with a specific probability.

Examples of continuous variables are the following:

  • A person’s height, weight
  • Time taken to complete a task
  • Temperature

The most common way to represent continuous variables is through a scatter plot or a line graph. In a scatter plot, each point represents a data point, and the graph shows how the variable changes across different values.

Below are a few essential continuous variable characteristics:

  • Continuous variable changes over time.
  • Continuous variables can contain decimals.
  • Statisticians generally use line graphs and skews to visualize continuous variables. 

If you are looking for ways to understand statistics easily, I wrote a whole article where I share 9 helpful tips.

Discrete vs. Continuous Variables

Differences between Discrete and Continuous Variables

The main difference between discrete and continuous variables is that discrete variables can only take on specific values, whereas continuous variables can take on any value within a specified range. Discrete data is often referred to as categorical data, whereas continuous data is referred to as numerical data.

When using discrete data, the calculations used are often different from those used with continuous data. Due to their limited range of values, discrete variables are often analyzed using frequency distribution and mode, while continuous variables are analyzed using mean and standard deviation.

Discrete variables can only take on integer values, whereas continuous variables can take on any value within a range. Discrete variables are usually used when counting the frequency of specific events, while continuous variables help measure the intensity or magnitude of certain phenomena.

In terms of data analysis, discrete variables are typically analyzed using a frequency distribution table or bar chart, while continuous variables are analyzed using measures of central tendency and scatterplots.

Also, when dealing with categorical or limited-range data, discrete variables are used, while continuous variables are used when dealing with measurable data.

If you want to study the difference between discrete and continuous variables, you can check out Khan Academy, or if you enjoy watching a video discussing discrete and continuous variables and how they differ, I encourage you to watch the video below.

When to Use Discrete or Continuous Variables?

The choice between using a discrete or continuous variable will depend on the nature of the data and the research question under consideration. Generally, discrete variables are used when the data being analyzed is easy to count or takes on a finite set of values. On the other hand, continuous variables are used when the data being analyzed is measurable and can take on any value within a specified range.

For example, when analyzing the number of customers visiting a shop each day, discrete variables such as the number of customers can be used. However, in analyzing the amount of money spent by customers at the shop, continuous variables such as the total money spent are more appropriate.

Moreover, if the purpose of the study is to identify patterns or trends, using continuous variables would be the best approach.

What to read next:

Wrapping Up

The major difference between discrete and continuous variables is their ability to take on specific values. Discrete variables can take only finite and countable values, while continuous variables can take an infinite number of values within a range.

I believe that by understanding the fundamental differences, students and researchers can make informed decisions on which variable type to use and how to analyze the data.

In terms of statistical analysis, I believe that it is essential to choose the right variable type and representation to ensure accurate conclusions and meaningful insights.

Altiné

I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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