Chapters
Types of Quantitative Variables
In the previous sections, we learned about the difference between qualitative and quantitative variables. In the following sections, you’ll learn about how even within these two types of variables, there are different types of values. Here, we’ll focus on the differences found within quantitative variables, which can be either discrete or continuous.
What Are Discrete and Continuous Variables?
On April 10, 2019, the Event Horizon Telescope Collaboration made history. During their worldwide press conference, they unveiled the first image ever taken by humans of a black hole. The Event Horizon Telescope, or EHT for short, combined data from many observatories around the world in order to create the perfect telescope for capturing such a distant object.
Katie Bouman, a computer scientist specializing in the field of computer imagery, was a seminal figure in the creation of the algorithm that would be used for capturing images of black holes. Bouman, like many scientists, had to combine skills from many different disciplines in order to accomplish what was once thought of as impossible. One of these disciplines was, of course, statistics.
Algorithms involved in statistics are generally the same as in computer science - at their most basic, they are simply a set of instructions, usually given to a computer, in order to solve a problem. In the majority of cases, algorithms depend on a fundamental understanding of the different types of quantitative and qualitative variables. While qualitative variables can be divided into nominal and ordinal variables, quantitative variables fall under two distinct categories: discrete and continuous.
Quantitative variables, unlike qualitative variables, are those that are numeric. They typically involve measuring a quantity in a person, place or thing. The easy way to remember the difference between qualitative and quantitative variables is that one measures the qualities of something while the other measures quantities of something. Quantitative variables are also called numeric variables because they often carry numeric information.
Because quantitative variables strive to measure quantities, they are generally divided into discrete and continuous variables. The definition for a discrete variable is that it is countable, finite and numeric. Meaning, it is a number with an identified minimum and maximum.
Continuous variables, on the other hand, are defined as numbers or a numeric date that can take on any value. A numeric date means, for example, 01/01/2019 as opposed to names for days of the week or for months.
Here are some examples that can help you better understand.
Discrete Variables
An example of a discrete variable can be the number of students in a classroom of 50 students. The minimum is 0 students and the maximum is 50. Let’s say that you decide to record the number of students that show up every day to class. The first day, 20 students are present. The next day, 25 students attend class, and so on. Why is this a discrete variable?
The number of students in this classroom is finite, meaning we know that the total number of students ends at 50. At the same time, we also know they are countable - you can’t count 1.5 of a student or 3/4ths of a student.
Some other examples of discrete variables can be:
- Number of books published in a year
- Number of clothing items in your closet
- Number of protesters at a rally
Continuous Variables
An example of a continuous variable can be height. If you were to measure the 50 students’ heights used in the previous example, there would be an infinite number of possibilities. Even if you measure the minimum and maximum heights of these students, you still wouldn’t be able to guess all the possible heights they could be. In other words, height is not a countable variable.
Take a look at your own height. Assume you have the most advanced measuring device in the world, which lets you measure heights to any decimal place you like. You know that you’re between 160 and 163 centimetres but want to know your precise height. At the first decimal place, your device reads 160.3 cm. Take it to two decimal places, it reads 160.31 cm. You see where we’re going. Between 160 cm and 163 cm, there are an infinite, or uncountable, number of possibilities: 160.45, 160.99999, 162.543.
Some other examples of continuous variables are:
- Weight
- Time it takes to complete a task
- Speed of a car
Please Note:
A qualitative variable can also be discrete, but it can never really be continuous. For example, you’re measuring the colours of one stoplight at an intersection. The colours, red, yellow and green, can be expressed as numbers, 1, 2, and 3. In this instance, this variable is discrete: 1.5 wouldn’t make sense, as there is no possible way for the stoplight to take on red and half yellow.
Problem 1: Discrete versus Continuous Variables
We have measured certain quantitative variables in a classroom. Before you do anything with the data you’ve collected, you must label your variables as either discrete or continuous. Fill in the table below with your answer and, afterwards, check the solution provided below.
| Variable Name | Type of Variable |
| Number of books in the classroom | |
| Time it takes for students to finish their lunch | |
| Age in years | |
| Numeric date of birth | |
| Shoe size | |
| Number of students that bring their lunch to school |
Solutions to Problem 1
In this problem, you were asked to identify whether a variable given is discrete or continuous. In the table below, you’ll find the answers.
| Variable Name | Type of Variable |
| Number of books in the classroom | Discrete |
| Time it takes for students to finish their lunch | Continuous |
| Age | Discrete |
| Numeric date of birth | Discrete |
| Shoe size | Discrete |
| Number of students that bring their lunch to school | Discrete |
Focusing on age, date of birth and shoe size - these variables could also be continuous depending on whether or not an exact measurement was recorded. No two people are the same age unless they’re born at the same moment, so you could have two people who are 24, but who are technically 24.3 and 24.7. The same can be said for date of birth, which can be measured to hours and seconds, and shoe size.
Univariate, Bivariate and Multivariate Analysis
Now that you know the most common types of variables, it’s important to note what kind of statistical analysis you can perform. Statistical analysis is defined by studying the relationship between variables and can by univariate, bivariate or multivariate analysis. Below, you will find the definitions and descriptions for each.
| Type | Univariate Analysis | Bivariate Analysis | Multivariate Analysis |
| Definition | When you study one variable, you are performing a univariate analysis. | When you study two variables and the relationship between them. | Studying two or more variables and the relationships between them. |
| Trick for remembering | Uni is the prefix for “one.” Think of words like unison, which is a singular action or performance, and unicorn, which has one horn. | Bi is the prefix for “two.” It’s helpful to think of words like bilingual, which means speaking two languages. | Multi means “many.” This is simple to remember thanks to words like multiple or multitude, all of which mean many. |
| Example | Examining the number of students that come to class. Here, there is one variable: number of students. | Investigating the number of students that come to class and their grades. Here, there are two variables and we can measure to what degree the number of students present relates to grades. | Looking at the number of students that come to class, their grades, age. Here, we can analyse any relationships between these 3 variables. |
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