Categorical Data
Let us observe the following situation before starting:
The following pie chart depicts the results of a random poll on the choice of holiday locations of people in a city.
Since the above recorded data includes the names of different types of locations under one category, will it be considered as categorical data?
It also has a percentage value of preferences for different locations which includes numerical data, so would it be considered as numerical data?
To find the answers to the above questions, check out this minilesson.
In this chapter, you will learn about categorical data examples, the distinction between categorical and numerical data, categorical data meaning, and the types of categorical data.
Check out the interactive examples and try your hand at solving a few practice questions at the end of the page.
Lesson Plan
What Is Categorical Data?
Data is the term used to refer to a set of raw information gathered for a specific purpose.
Typically, data is divided into two categories. They are:
 Numerical Data (quantitative data)
 Categorical Data (qualitative data)
Categorical Data Meaning
Categorical data is the data grouped in the form of categories.
The grouping is done based on the qualitative aspects of the gathered raw information.
These qualitative aspects can include colors, age groups, food cuisines, sports, genders, shapes, etc.
This doesn't mean that categorical data has no relation with numerical values.
In some cases, categorical data might include numerical values to define the quantity of the grouped data.
Categorical Data Examples
The following images show how categorical data are grouped together.
Different seasons share a common category called "seasons."
Similarly, tshirts of different sizes can be grouped together under the category "tshirts."
The following table shows examples of categories and the objects under them.
Category  Examples 

Hair colors  
Perfume brands  
Age groups  
Film Genres  
Festivals 

What Are the Types of Categorical Data?
There are two types of categorical data.
 Nominal categorical data
 Ordinal categorical data
Nominal categorical data
The word "Nominal" is derived from the Latin word "Nomen", which means name.
Thus, nominal categorical data includes "named" or "labeled" data, which does not take the numerical values of the data into consideration.
Examples include different writing genres like fiction and scifi, varieties of flowers, color hues, etc. are examples of nominal categorical data.
Ordinal categorical data
Ordinal categorical data has a certain "scale" or "measure" for the data grouped together.
The scale might not always be specific or standard.
This kind of data is generally ordered or measured.
Due to the presence of numerical values, this type of categorical data is said to exhibit the properties of both categorical data and numerical data.
They can be analyzed through grouping and they can be visually represented using bar graphs.
Examples include surveys that take numerical values into analysis for comparing grouped data under categorical variables.
The following pie chart depicts the results of a random poll on the choice of holiday locations of people in a city.
What Is a Categorical Variable?
A categorical variable is a variable that takes different values under different names or labels under grouped categorical data.
A categorical variable serves as the basic attribute of the data classified under a specific category.
Examples
Different shades of color, luxury brands, blood groups of a person, etc. are examples of categorical variables.

Numbers can be included in categorical data. Numbers representing certain common labels and the numerical analysis of categorical data can be a part of grouping under categorical data.
Solved Examples
Example 1 
Anna is learning to classify objects under categorical data.
Can you help her name 3 categorical variables for the following object?
Solution
Anna can categorize the above object under the following categorical variables:
 Cylinders
 Geometrical shapes
 Purplecolored objects
Example 2 
The following table depicts the percentage of people who prefer a certain movie genre.
Can you represent this categorical data using a pie chart?
Movie Genre  Percentage of people 

Comedy 
20% 
Romance 
30% 
Action 
25% 
Drama 
5% 
SciFi 
20% 
Solution
The above grouped categorical data can be depicted using a pie chart as:
Example 3 
Can you help Amanda differentiate between nominal and ordinal categorical data?
Solution
The following table lists the differences between nominal and ordinal categorical data.
Nominal Categorical Data  Ordinal Categorical Data 

1. It is a group of nonparametric and nonordered data. 
1. It is a group of nonparametric ordered data. 
2. The values are categorized as nominal based on their "names" or ''labels." 
2. The values are categorized as ordinal on the basis of their numerical data. 
3. Nominal categorical data is used to group similar objects under a similar category. 
3. Ordinal categorical data is used to carry out analyses or studies on people's views or opinions. 
4. Examples: Hair color, gender, country, race, etc. 
4. Examples: The different positions secured by students in an examination, people's views on a survey, etc. 
Example 4 
Ryan is studying how to sort nominal categories into desired groups.
Can you help him put the following colors into specific sections?
Solution
The above colors can be arranged into nominal categorical data as shown below:
Pink shade  Green shade  Blue shade  Yellow shade 

Example 5 
The following bar graph depicts the ordinal categorical data of the number of students whose birthdays fall on respective months.
Can you answer the following questions based on your observations of the graph?
 What is the total strength of students?
 Find the average of the three months with the most number of birthdays.
 Find the average of the four months with the least number of birthdays.
Solution
Based on the observations made from the bar graph:
Total number of students = 3 + 4 + 2 + 3 + 8 + 10 + 6 + 1 + 7 + 8 + 4 + 7 = 63 students
Average of the three months with the most number of birthdays = \( \frac{ 10 + 8 + 8 }{ 3 } = 8.667 \)
Average of the four months with the least number of birthdays = \( \frac{1 + 2 + 3 + 3}{ 4} = 2.25 \)
 How would you differentiate numerical data from ordinal data?
Interactive Questions
Here are a few activities for you to practice.
Select/Type your answer and click the "Check Answer" button to see the result.
Let's Summarize
The minilesson targeted the fascinating concept of categorical data. The math journey around categorical data starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.
About Cuemath
At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!
Through an interactive and engaging learningteachinglearning approach, the teachers explore all angles of a topic.
Be it problems, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.
Frequently Asked Questions (FAQs)
1. Can number be categorical data?
Yes, numbers can be included as categorical data.
Numbers representing certain common labels and the numerical analysis of categorical data can be a part of grouping under categorical data.
2. Is a year considered as a categorical variable?
Yes, a year can be considered as a categorical variable.
Different months can be considered as categorical data.
3. Is age considered as nominal or ordinal categorical data?
Age can be categorized both as nominal and ordinal based on the usage.
Age, when used to depict certain order, comes under ordinal categorical data.
Nominal categorical data includes "named" or "labeled" data, which does not take the numerical values of the data into consideration.
Age as an aspect without comparison based on the order of numerical data comes under nominal categorical data.