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
Categorical data is data that can be sorted into groups or categories, like colors, types, or names, rather than measured with numbers. You can count how many items fall into each category, but you cannot meaningfully add, subtract, or average the category labels themselves.
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 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 starts by naming the question and variable before any graph or summary is chosen.
Common stuck point:Students often know a procedure related to categorical data but skip the recognition step: Have I named the variable, the possible responses, and the reason the responses may vary? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Have I named the variable, the possible responses, and the reason the responses may vary?
Worked Examples
Example 1
medium
Of 40 students, 25% chose pizza, 30% chose burgers, and the rest chose tacos. How many chose tacos?
Answer
18
First step
1
Pizza =0.25×40=10.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
A teacher records 100 transportation choices: walk 18, bike 22, bus 36, car 24. Which category accounts for the largest fraction, and what is that fraction in simplest form?Which category has the largest fraction? Express that fraction in simplest form.
Example 3
medium
Which of these is NOT categorical data: A) eye color, B) sport, C) test score? Answer 1=A, 2=B, 3=C.
Example 4
challenge
A school records 250 birthday months. If each month is a category, what is the minimum possible count for the most-popular month (the mode), assuming counts can be any non-negative whole numbers?
Example 5
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.
Example 6
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
easy
Which is categorical: eye color or height in cm? Answer 1 for eye color, 2 for height.
Example 2
easy
Pet survey: cat, dog, cat, cat, dog. How many cats (a category count)?
Example 3
easy
Is 'favorite color' categorical or numerical? Answer 1 for categorical, 0 for numerical.
Example 4
easy
In categories dog, cat, bird with counts 4, 2, 3, how many distinct categories are there?
Example 5
easy
Which can you NOT average: shoe sizes or shirt colors? Answer 1 for shirt colors, 2 for shoe sizes.
Example 6
easy
Survey of fruit: apple, banana, apple, apple, banana. How many bananas?
Example 7
easy
Is 'type of transport (bus, car, bike)' categorical? Answer 1 for yes, 0 for no.
Example 8
easy
Categories red, blue, green have counts 5, 5, 4. Which category has the most? Answer with its count.Which category has the most responses? Answer with its count.
Example 9
medium
A survey of 50 students records favorite subject. Math 18, Science 14, Art 11, the rest English. How many chose English?50 students chose their favorite subject. How many chose English?
Example 10
medium
In a class, 12 like dogs and 8 like cats as their one favorite pet. What fraction like cats? Give a simplified fraction.
Example 11
medium
Four categories have counts 6, 9, 5, 10. What is the difference between the largest and smallest category count?
Example 12
medium
A survey lists 30 responses across 5 categories with equal counts. How many responses per category?
Example 13
medium
Of 40 pets surveyed, 25 percent are birds. How many birds (a categorical count)?
Example 14
medium
Two categories, A and B, have counts in ratio 3:2 and total 35. How many are in category A?
Example 15
challenge
A survey of 60 has categories in ratio 2:3:5. How many more are in the largest than the smallest category?
Example 16
challenge
In a survey, 3/5 chose fiction and the remaining 16 chose nonfiction. How many people were surveyed in total?
Example 17
challenge
Categories P, Q, R have counts where Q is twice P and R is 5 more than Q. If P = 4, what is the total?
Example 18
medium
A survey of 36 has categories in ratio 1:2:3. How many are in the smallest category?
Example 19
medium
A class survey has 18 in category X out of 45 total. What fraction is X? Give a simplified fraction.
Example 20
medium
Five categories share 35 responses equally. How many per category?
Example 21
easy
Which is categorical data: 'favorite ice cream flavor' or 'temperature in degrees'? Answer 1 for flavor, 2 for temperature.
Example 22
easy
Pet survey: rabbit, hamster, rabbit, fish, rabbit, hamster. How many rabbits?
Example 23
easy
Is 'type of shoe (sneaker, sandal, boot)' categorical? Answer 1 for yes, 0 for no.
Example 24
easy
A class lists 4 favorite seasons with counts 5, 8, 6, 7. How many distinct categories are listed?
Example 25
easy
Survey of fruit: apple, pear, apple, apple, pear, kiwi, kiwi. How many apples?
Example 26
easy
Categories red, blue, green, yellow have counts 4, 7, 3, 6. What is the total?Find the total count across all four color categories.
Example 27
easy
Which question collects categorical data: 'How many siblings?' or 'What language do you speak at home?' Answer 1 for siblings, 2 for language.
Example 28
medium
A survey of 60 students lists favorite subject. Math 22, Science 17, Art 13, the rest English. How many chose English?60 students chose a favorite subject. How many chose English?
Example 29
medium
In a class, 14 like dogs, 6 like cats, and 5 like fish as their one favorite pet. What fraction like dogs? Give a simplified fraction.What fraction of the class chose dog as their favorite pet?
Example 30
medium
Five categories have counts 8, 11, 6, 14, 9. What is the difference between the largest and smallest category count?
Example 31
medium
Categories A, B, C have counts 3x, 2x, 5x. If the total is 50, what is x?
Example 32
medium
A class of 30 chose a vacation type: 12 beach, 9 mountains, the rest city. What fraction chose city? Simplify.
Example 33
medium
Categories of book genres show counts 14, 9, 7, 10. What is the mode category's count?
Example 34
hard
A school of 200 students recorded primary lunch choice: 35% pasta, 25% sandwich, 20% salad, the rest soup. How many chose soup?
Example 35
hard
A survey shows category ratios A:B:C =2:3:5 with total 80 responses. How many in category B?
Example 36
hard
A class chose a pet category: 8 dog, 6 cat, 4 fish, 2 bird. What percent of the class chose cat? Round to the nearest whole percent.What percent of the class chose cat as their favorite pet?
Example 37
medium
Of 36 students, 41 ride the bus, 31 walk, the rest are driven. How many are driven?
Example 38
easy
A pet survey records dog, cat, dog, fish, bird, dog, cat. How many distinct categories appear?
Example 39
challenge
A survey shows ratios for favorite color red:blue:green:yellow =4:5:3:2. If 35 students chose blue, how many total students were surveyed?
Example 40
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 41
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.