Categorical Data Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Categorical Data.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Data that can be sorted into groups or categories, like colors, types, or names, rather than measured with numbers.

Categorical data puts things in boxes by type, not by how much. Your favorite color, pet type, or sport are categories - you can't average them, but you can count how many in each group.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Categorical data puts observations into named groups. You can count how many are in each group, but you cannot add, subtract, or average the group names.

Common stuck point: Using numerical codes for categories (e.g., 1=male, 2=female) tricks students into calculating a meaningless mean of the codes.

Worked Examples

Example 1

easy
Classify each of the following as categorical or numerical data: (a) Favourite pizza topping, (b) Height in centimetres, (c) Eye colour, (d) Number of siblings.

Solution

  1. 1
    Step 1: Categorical data consists of labels or names that describe qualities — they cannot be meaningfully averaged or ordered numerically.
  2. 2
    Step 2: Numerical data consists of numbers that represent measurements or counts and can be ordered and averaged.
  3. 3
    Step 3: Apply: (a) Favourite pizza topping — labels/names → categorical. (b) Height in cm — measurement → numerical. (c) Eye colour — labels → categorical. (d) Number of siblings — count → numerical.

Answer

(a) Categorical, (b) Numerical, (c) Categorical, (d) Numerical.
Categorical data describes qualities or categories (like colour, type, or preference) while numerical data represents quantities that can be measured or counted. Recognising the data type is essential for choosing appropriate graphs and statistical measures.

Example 2

medium
A survey asks: 'Rate your satisfaction: Very Unsatisfied, Unsatisfied, Neutral, Satisfied, Very Satisfied.' Is this categorical or numerical data? Can you calculate a mean satisfaction score?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A student collects data on 20 classmates: shoe size, favourite subject, number of pets, and birth month. Which variables are categorical and which are numerical? For each categorical variable, state the most appropriate graph to display it.

Example 2

hard
A researcher records the following for 100 cars: colour (red, blue, white, black, other), fuel type (petrol, diesel, electric, hybrid), and fuel efficiency (km/L). (a) Identify all categorical variables. (b) Can the researcher find a correlation between colour and fuel type? Explain.
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Related Concepts

Bar Graph

Background Knowledge

These ideas may be useful before you work through the harder examples.

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