# Categorical vs. Quantitative Variables: Definition + Examples

In statistics, variables can be classified as either categorical or quantitative.

Categorical Variables: Variables that take on names or labels. Examples include:

• Marital status (“married”, “single”, “divorced”)
• Smoking status (“smoker”, “non-smoker”)
• Eye color (“blue”, “green”, “hazel”)
• Level of education (e.g. “high school”,  “Bachelor’s degree”, “Master’s degree”)

Quantitative Variables: Variables that take on numerical values. Examples include:

• Height of an individual
• Population size of a city
• Number of students in a class
• Number of square feet in a house

The following table summarizes the difference between these two types of variables: ### Examples: Categorical vs. Quantitative Variables

Use the following examples to gain a better understanding of categorical vs. quantitative variables.

Example 1: Plant Height

A botanist walks around a local forest and measures the height of a certain species of plant. The variable plant height is a quantitative variable because it takes on numerical values. For example, the height could be 15 inches, 17.5 inches, 19.2 inches, etc.

Example 2: Vacation Locations

A researcher surveys 200 people and asks them about their favorite vacation location. The variable vacation location is a categorical variable because it takes on names. For example, responses could include “Miami”, “San Francisco”, “Hilton Head”, etc.

Example 3: Political Party

A political scientists surveys 50 people in a certain town and asks them which political party they identify with. The variable political party is a categorical variable because it takes on labels. For example, responses could include “Democrat”, “Republican”, “Independent”, etc.

Example 4: Running Times

A coach records the running times of his 20 track runners. The variable running time is a quantitative variable because it takes on numerical values. For example, running time could be 58 seconds, 60.343 seconds, 65.4 seconds, etc.

Example 5: House Prices

An economist collects data about house prices in a certain city. The variable house price is a quantitative variable because it takes on numerical values. For example, house price could be \$149,000, \$289,000, \$560,000, etc.

### How to Describe Categorical & Quantitative Variables

We can summarize categorical variables by using frequency tables.

For example, suppose we collect data on the eye color of 100 individuals. Since “eye color” is a categorical variable, we might use the following frequency table to summarize its values: We can summarize quantitative variables using a variety of descriptive statistics.

For example, suppose we collect data on the square footage of 100 homes. Since “square footage” is a quantitative variable, we might use the following descriptive statistics to summarize its values:

• Mean: 1,800
• Median: 2,150
• Mode: 1,600
• Range: 6,500
• Interquartile Range: 890
• Standard Deviation: 235

These metrics give us an idea of where the center value is located as well as how spread out the values are for this variable.