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Categorical Data
Categorical data represents the qualitative information (data) that is divided into distinct categories or groups rather than numerical values. It can be nominal or ordinal. Since categorical data does not have arithmetic operations, it is analyzed using frequency counts, percentages, and it is visualized with bar charts, or pie charts.
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What is Categorical Data?
Categorical data is the data that can be represented as categories or data which can be grouped. It stores data into categories or groups using names or labels. Categorical data is most commonly called qualitative data. It is visually represented by using bar charts, pie charts or frequency tables.
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What are the Types of Categorical Data?
There are two main types of categorical data and they are as follows:
- Nominal Data
- Ordinal Data
Let us now see what they mean:
Nominal Data:
Nominal data is the type of categorical data that consists of two or more categories without any kind of specific order. Nominal data cannot be quantified that is put into a definite hierarchy. Variables without any quantitative value or order are labelled using nominal data.
Ordinal Data:
Ordinal data is the type of categorical data that consists of categories with a natural rank order. However, the difference between the ranks may not be equal. Ordinal data is a statistical type of data which is quantitative, where variables exist in naturally occurring ordered categories.
What are the properties of Categorical Data
There are lots of different properties for categorical data. Let us see some important properties of categorical data:
Qualitative in Nature:
Categorical data consists of labels, names, or categories rather than numerical values.
No Arithmetic Operation:
Unlike numerical data, mathematical operations such as addition, subtraction, or averaging cannot be applied.
Can be Nominal or Ordinal:
Nominal Data: Categories have no inherent order.
Ordinal Data: Categories have no defined interval in the order.
Represented Using Labels:
Values in categorical data are represented as text or symbols are used rather than numbers.
How to calculate categorical data
To calculate the categorical data, we must follow the steps mentioned below:
Step 1: Collect the Categorical Data:
First, we have to identify and gather the categorical data from different sources.
Then, we have to ensure that the data is organized in distinct categories.
Step 2: Organize the data into Frequency Table:
List each category along with the frequency of each category.
Step 3: Visualize the Data:
Use bar charts, pie charts, or histograms to represent categorical data.
Step 4: Analyze the Mode:
The mode is the category with the highest frequency.
Step 5: Use Contingency Tables for Two Categorical Variables:
If analyzing relationships between two categorical variables, use contingency table
Real life applications on Categorical Data
The categorical data have numerous applications across various fields. Let us explore how the categorical data is used in different areas:
Healthcare:
We use categorical data in patient diagnoses, where we use it in checking medical conditions. For example, diabetes: yes/no.
Treatment preferences: Type of treatment received. For example, surveys, medication, therapy.
Hospital data analysis: Number of patients by gender and insurance type.
Marketing and Consumer Behavior:
In marketing and consumer behavior, businesses segment customers based on gender, location and shopping habits. Product preferences are also analyzed using categorical data.
Education:
Student performance is assessed by grouping students into grade categories like A, B, C, and D. Schools use categorical data to analyze course enrollments by subject streams such as science, arts and commerce.
Common mistakes and How to Avoid Them in Categorical Data
Students tend to make some mistakes while making frequency tables. Let us now see the different types of mistakes students make while creating frequency tables and their solutions:
Mistake 1
Ignoring Ordinal Nature of Data
Students must use appropriate methods for ordinal data, such as ordered logistic regression or median summary statistics, instead of treating them as purely categorical.
Mistake 2
Using Incorrect Visualization Method
Students must practice using appropriate visualizations like bar charts, pie charts, and frequency tables for categorical data instead of line plots or scatter plots.
Mistake 3
Overlooking Missing Data
Students must handle missing data properly by using mode imputation for nominal data and ordinal interpolation for ordinal data, or clearly marking them as unknown if necessary.
Mistake 4
Incorrect Label Encoding
Students must use one-hot encoding for nominal data instead of encoding. For ordinal data, ensure the encoding preserves the correct ranking order.
Mistake 5
Ignoring Category Imbalance
Students should use weighted sampling techniques or undersampling and oversampling methods to balance category distributions before analysis.
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Solved questions on Categorical Data
Problem 1
You have a list of responses for gender from a survey: [male, female, female, male, male]. Count the frequency for each category.
Male: 3
Explanation
List the data:
Data: male, female, female, male, male.
Count each category:
Male: 3
Female: 2
Problem 2
Given the dataset of colors: ["Red", "Blue", "Green", "Red", "Red", "Blue"], determine the mode.
Mode: Red
Explanation
Count each color:
Red: 3
Blue: 2
Green: 1
Identify the most frequently occurring value:
Mode is “Red”.
Problem 3
A survey collected responses: ["Yes", "No", "Yes", "Maybe", "No", "Yes", "No", "Maybe"]. Construct a frequency distribution table.
| Response | Frequency |
| Yes | 3 |
| No | 3 |
| Maybe | 2 |
| Total | 8 |
Explanation
Count the responses:
Yes: 3
No: 3
Maybe: 2
Create the table
The above table shows the organized data with corresponding frequency counts.
Problem 4
You have two categorical variables: Gender (Male, Female) and Beverage Preference (Tea, Coffee). The data collected is: "Male, Tea" "Female, Coffee" "Female, Tea" "Male, Coffee" "Female, Tea" "Male, Tea" Create a contingency table.
| Tea | Coffee | Total | |
| Male | 2 | 1 | 3 |
| Female | 2 | 1 | 3 |
| Total | 4 | 2 | 6 |
Explanation
Tally the data:
Male, Tea: Occurs in observations 1 and 6 → 2
Male, Coffee: Occurs in observation 4 → 1
Female, Tea: Occurs in observations 3 and 5 → 2
Female, Coffee: Occurs in observation 2 → 1
Create the table
A contingency table shows the frequency of each combination of the two categorical variables.
Problem 5
A survey records favorite pets from 10 respondents: ["Dog", "Cat", "Dog", "Fish", "Cat", "Dog", "Bird", "Cat", "Dog", "Cat"]. Summarize the data by creating a frequency distribution.
| Favorite Pet | Frequency |
| Dog | 4 |
| Cat | 4 |
| Fish | 1 |
| Bird | 1 |
| Total | 10 |
Explanation
Count each category:
Dog: 4
Cat: 4
Fish: 1
Bird: 1
Create the frequency table:
This table provides a clear summary of the survey responses by counting each pet category.
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FAQs on Categorical Data
1.What is categorical data?
2.What are examples of categorical data?
3.What is nominal data?
4.What is ordinal data?
5.How do you represent categorical data graphically?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
