What is a quantitative variable that could have an infinite number of values?

Data can be understood as the quantitative information about a specific characteristic. The characteristic can be qualitative or quantitative, but for the purpose of statistical analysis, the qualitative characteristic is transformed into quantitative one, by providing numerical data of that characteristic. So, the quantitative characteristic is known as a variable. Here in this article, we are going to talk about the discrete and continuous variable.

Content: Discrete Variable Vs Continuous Variable

Comparison Chart

Basis for ComparisonDiscrete VariableContinuous VariableMeaningDiscrete variable refers to the variable that assumes a finite number of isolated values.Continuous variable alludes to the a variable which assumes infinite number of different values.Range of specified numberCompleteIncompleteValuesValues are obtained by counting.Values are obtained by measuring.ClassificationNon-overlappingOverlappingAssumesDistinct or separate values.Any value between the two values.Represented byIsolated pointsConnected points

Definition of Discrete Variable

A discrete variable is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order.

Also known as a categorical variable, because it has separate, invisible categories. However no values can exist in-between two categories, i.e. it does not attain all the values within the limits of the variable. So, the number of permitted values that it can suppose is either finite or countably infinite. Hence if you are able to count the set of items, then the variable is said to be discrete.

Definition of Continuous Variable

Continuous variable, as the name suggest is a random variable that assumes all the possible values in a continuum. Simply put, it can take any value within the given range. So, if a variable can take an infinite and uncountable set of values, then the variable is referred as a continuous variable.

A continuous variable is one that is defined over an interval of values, meaning that it can suppose any values in between the minimum and maximum value. It can be understood as the function for the interval and for each function, the range for the variable may vary.

Key Differences Between Discrete and Continuous Variable

The difference between discrete and continuous variable can be drawn clearly on the following grounds:

1. The statistical variable that assumes a finite set of data and a countable number of values, then it is called as a discrete variable. As against this, the quantitative variable which takes on an infinite set of data and a uncountable number of values is known as a continuous variable.
2. For non-overlapping or otherwise known as mutually inclusive classification, wherein the both the class limit are included, is applicable for the discrete variable. On the contrary, for overlapping or say mutually exclusive classification, wherein the upper class-limit is excluded, is applicable for a continuous variable.
3. In discrete variable, the range of specified number is complete, which is not in the case of a continuous variable.
4. Discrete variables are the variables, wherein the values can be obtained by counting. On the other hand, Continuous variables are the random variables that measure something.
5. Discrete variable assumes independent values whereas continuous variable assumes any value in a given range or continuum.
6. A discrete variable can be graphically represented by isolated points. Unlike, a continuous variable which can be indicated on the graph with the help of connected points.

Examples

Discrete Variable

• Number of printing mistakes in a book.
• Number of road accidents in New Delhi.
• Number of siblings of an individual.

Continuous Variable

• Height of a person
• Age of a person
• Profit earned by the company.

Conclusion

By and large, both discrete and continuous variable can be qualitative and quantitative. However, these two statistical terms are diametrically opposite to one another in the sense that the discrete variable is the variable with the well-defined number of permitted values whereas a continuous variable is a variable that can contain all the possible values between two numbers.

Last but not least, in datasets it is very often the case that numbers are used for qualitative variables. For instance, a researcher may assign the number “1” to women and the number “2” to men (or “0” to the answer “No” and “1” to the answer “Yes”). Despite the numerical classification, the variable gender is still a qualitative variable and not a discrete variable as it may look. The numerical classification is only used to facilitate data collection and data management. It is indeed easier to write the number “1” or “2” instead of “women” or “men”, and thus less prone to encoding errors.

The same goes for the identification of each observation. Suppose you collected information on 100 students. You may use their student’s ID to identify them in the dataset (so that you can trace them back). Most of the time, students’ ID (or ID in general) are encoded as numeric values. At first sight, it may thus look like a quantitative variable (because it goes from 1 to 100 for example). However, ID is clearly not a quantitative variable because it actually corresponds to an anonymized version of the student’s first and last name. If you think about it, it would make no sense to compute the mean or median on the IDs, as it does not represent a numerical measurement (but rather just an easier way to identify students than with their names).

If you face this kind of setup, do not forget to your variable into the right type before performing any statistical analyses. Usually, a basic descriptive analysis (and knowledge about the variables which have been measured) prior to the main statistical analyses is enough to check that all variable types are correct.

Thanks for reading. I hope this article helped you to understand the different types of variable. If you would like to learn more about the different data types in R, read the article “Data types in R”.

As always, if you have a question or a suggestion related to the topic covered in this article, please add it as a comment so other readers can benefit from the discussion.

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