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Categorical variables are variables that can be divided into discrete categories, such as gender, race, or product type. Quantitative variables are variables that can be measured or counted, such as height, weight, or number of items sold. Categorical variables can be further divided into binary variables (i.e. yes/no, true/false) and nominal variables (i.e. names, labels), while quantitative variables can be divided into discrete and continuous variables (i.e. integers and decimals).
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.
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 is located as well as how the values are for this variable.
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