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Quantitative and Categorical Variables

(Harvard University - Joyce Yang)

- Overview

Quantitative variables and categorical variables are two types of data that play different roles in data analysis.

Variables can be divided into categorical variables and quantitative variables. Categorical variables are those that provide groupings that may not have a logical order, or where the logical order differs inconsistently between groups (e.g., the difference between first and second place in a race is not equal to the difference between third and fourth place in a race )). Quantitative variables have numerical values ​​with consistent intervals. 

  • Categorical variables: Names or labels (i.e., categories) that have no logical order or have a logical order but inconsistent differences between groups (such as rankings) are also called qualitative.
  • Quantitative variables: A numeric value whose size can be arranged at consistent intervals in a meaningful order is also called a numeric value.


Sometimes categorical data is represented with a number, but that number doesn't have a mathematical meaning. For example, January can be represented by the number 1, and February by 2, but it doesn't make sense to perform mathematical operations on them.

Please refer to the following for more information:


- Some Examples

Quantitative variables represent amounts or counts, while categorical variables represent groupings. 

Here are some examples of quantitative variables: 

  • Age
  • Number of children
  • Income
  • Plant height

Here are some examples of categorical variables: 

  • Type of pet
  • Agreement rating
  • Brand of shoes
  • Finishing places in a race
  • Brands of cereal
  • Coin flips


A general rule of thumb is that if you can add it, it's quantitative. For example, a G.P.A. of 3.3 and a G.P.A. of 4.0 can be added together (3.3 + 4.0 = 7.3), so that means it's quantitative. 


- Categorical vs. Quantitative Data: Why They’re So Valuable

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age). Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

In business, both categorical and quantitative data are valuable for gaining insights into customer behavior and demographics.

Here are some differences between categorical and quantitative data: 

  • Categorical data: Provides descriptive information about qualitative attributes. It's used to qualify information before classifying it according to similarities. For example, an organization's employee biodata is categorical data. This data can be grouped by variables like sex and state of residence.
  • Quantitative data: Offers numerical values for measuring and analyzing quantities. It's relatively quick and easy to collect, and it's easier to draw conclusions from. For example, quantitative variables include height, weight, and age.


Understanding the differences between categorical and quantitative data is essential for accurate and meaningful data interpretation. 

While categorical data provides descriptive information about qualitative attributes, quantitative data offers numerical values for measuring and analyzing quantities. Understanding the differences between these two data types is essential for accurate and meaningful data interpretation.


- Continuous and Discrete Variables

In mathematics and statistics, a quantitative variable can be either continuous or discrete.

A discrete variable is a variable that can only take on a limited number of values, such as only whole numbers. For example, the number of people in a family or the number of students in a class are discrete variables. 

A continuous variable is a variable that can take on any value and any value between two values. For example, a spectrum of real numbers is a continuous variable.

Discrete variables are used for counting, and continuous variables are used for measuring. For example, in an experiment where the random variable is defined as the number of coin flips until the first head, the range is infinite but still countable.

Discrete data is often represented using tally charts, bar charts, or pie charts.


[More to come ...]

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