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In the other sections of this guide on descriptive statistics, we reviewed all the different types of variables you’re likely to encounter in statistics. From distinguishing between numerical and categorical variables to understanding ordinal and nominal ones, remembering how each is defined can be difficult. Here you’ll find a brief overview of the most common statistical variables.

## Types of Variables

Variables are an integral part of statistics - after all, what is statistics without variables? A variable is defined as any numerical or categorical place, individual or thing that is measured. Variables can take on almost anything, from the number of cars in a parking lot to the level of carbon dioxide in the atmosphere.

Variables can be both tangible and intangible - meaning, variables can be something physical or something not physical. Take a look at the table below in order to get a better idea of what physical and non-physical variables look like.

 Variable Type Description Example Intangible A non-physical quality, characteristic, idea A person’s kindness Tangible A physical quality, characteristic A person’s height

Intangible and tangible don’t necessarily refer to a variable’s ability to be measured. For example, while a person’s kindness can’t be directly measured, you could use what’s called a proxy variable.

Proxy variables are those which are measured in order to approximate or take the place of other variables. For example, we could measure kindness through the proxy variable of the amount donated each year or the amount of time spent volunteering in a month.

Likewise, tangible doesn’t always mean measurable. While the heat of the sun is tangible, that doesn’t necessarily mean scientists have the ability to measure it directly.

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## Quantitative and Qualitative Variables

There are two main branches of variables in statistics: quantitative and qualitative variables. These are easy to distinguish because of the fact that quantitative variables measure quantities while qualitative variables measure qualities. Take a look at the table below for some clarification on the definitions of these two variable types.

 Variable Type Description Other Names Example Quantitative Measures quantities Numerical Speed in miles per hour Qualitative Measures qualities Categorical Favourite ice cream flavour

Qualitative variables are easily identifiable because of the fact that they are mostly, but not always, in the form of a string of characters. In other words, qualitative variables are often words or codes. Take a look at the table below to get an idea of what a mixture of qualitative and quantitative variables looks like.

 Variable Name Variable Type Number of Siblings Quantitative or Qualitative Name Qualitative Birthday Quantitative or Qualitative Age Quantitative

Notice that some variables can be quantitative or qualitative. Take number of siblings as an example. While this is a physical measure, think about the likelihood of the number of siblings a person has to be over 5, 10, or even 20.

Most likely, the number of siblings will very rarely go over 5 or 6, and so while it is quantitative variable, it can be treated as a qualitative variable if we equate the number of siblings to levels or if we group them. For example, we can have two groups, one that is “five siblings or less” and the other that is “more than five siblings.”

## Continuous and Discrete Variables

Within qualitative and quantitative variables, you will find discrete and continuous variables. While discrete variables can be both qualitative and quantitative, continuous variables are almost always just quantitative. You can find a comparison of continuous and discrete variables in the table below.

 Continuous Discrete Can take on an infinite amount of possibilities Can take on a finite amount of possibilities Is not countable Is countable Can be quantitative Can be quantitative or qualitative Not mutually exclusive categories (can overlap) Mutually exclusive categories

Discrete and continuous variables are often easily identifiable when looking at a data set but can be tricky to distinguish simply from looking at the variable name. Find some examples in the table below.

 Question Variable Type Variable Type Age Quantitative or Qualitative Continuous or Discrete Dog breed Qualitative Discrete Hair colour Qualitative Discrete Height Quantitative Continuous Birth Month Quantitative or Qualitative Continuous or Discrete

As you can see from the table above, variables are typically discrete when they are qualitative. This is an easy way to determine whether or not a variable is quantitative or qualitative. Take age, for example - if the ages were grouped into 10-year groups, there would be a discrete number of groups and, therefore, the variable would be qualitative.

## Ordinal and Nominal Variables

Ordinal and nominal variables, unlike discrete and continuous ones, can only ever be qualitative variables. Nominal variables are another way of saying categorical or qualitative variables. Nominal variables are typically what you think of when you see categorical variables. Their categories fall in no particular order.

Ordinal variables, on the other hand, are categorical variables whose categories do have a specific order. Take a look at the table below for a more detailed description of the differences between ordinal and nominal variables.

 Nominal Ordinal Variable with two or more categories Variable with two or more categories Order of the categories doesn’t matter Order of the categories does matter Examples Examples Hair colour Nationality Name Age group Satisfaction level Product rating

From the table above, you can see that the main difference between ordinal and nominal data is the fact that the categories in ordinal data lie on some sort of scale.

Take a look at the table below to understand the types of questions that can help you determine whether or not a categorical variable is ordinal or not.

 Categories on a Scale Based On: Description Worth Is one category valued higher than the other? (one letter grade valued higher than another) Preference Is one category more desirable than another? (a higher rating is more preferable than the other) Greatness Is one category better than another? (from the point of view of an employer, perhaps one education level would be desired over another)

## Problem 1

You need to sort out all the different variable types in your data set. Label each variable according to the three levels of classification we reviewed whenever possible. If you get stuck on any particular variable, make sure to review the rules and definitions we’ve described in this section.

 Variable Variable Type (Quantitative or Qualitative?) Variable Type (Continuous or Discrete?) Variable Type (Nominal or Discrete?) Exact Age (year, month and day) Hair Colour Grade Level Number of Siblings

## Solution Problem 1

In the table below, you will find the solution to problem 1. Keep in mind that in statistics, there is very rarely one blanket solution for a problem: context is everything. This is why we specified the variable “Exact Age” to be in years, months and days. Remember from previous examples that age can be quantitative or qualitative depending on how the data has been collected and is formatted.

For example, if you collected age data in years, you could be tempted to assume it is quantitative right off the bat. However, even if you collected data on over 1,000 people, perhaps their ages range only from 40 to 45. In that case, it may make sense to treat your age variable as a qualitative variable instead, with each range representing an “age level.”

 Variable Variable Type Variable Type Variable Type Exact Age (year, month and day) Quantitative Continuous Hair Colour Qualitative Discrete Nominal Grade Level Qualitative Discrete Ordinal Number of Siblings Quantitative Discrete

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