Categorical data are data that sort people or things into groups, or categories, such as eye color, favorite sport or a yes/no answer. The values are labels, not measurements, so you count how many fall in each category and show the counts with a bar graph, a pie chart or a two-way table.
In Spanish
datos categóricos
Also called
qualitative data, categorical variable, nominal data
Categorical answers are labels. You cannot add or average “apple” and “grape”, so you count each category and graph the counts.
Formal definition and notation
A categorical (qualitative) variable places each individual into one of several groups. Its values are names or labels, even when they are written as numbers, such as ZIP codes or jersey numbers, so arithmetic on them has no meaning. Categorical data are summarized with counts, percents or relative frequency in each category, and the mode is the only measure of center that applies. Data that are counts or measurements are quantitative (numerical) instead.
Symbol
Read it as
Meaning
f
frequency
the count of individuals in one category
fn
f over n
the relative frequency of a category out of n individuals
Key facts
Ask: does averaging the values make sense? If not, the data are categorical.
Numbers can be categories: ZIP codes, phone area codes and jersey numbers are labels.
Summarize with counts and percents. The mode (the most common category) is the only “average” that applies; there is no mean or median of eye colors.
Bar graphs for categorical data have gaps between the bars, unlike a histogram.
Two categorical variables together go in a two-way table, which can show an association.
Some categories have a natural order, such as small, medium, large; these are called ordinal.
Categorical Data examples, step by step
Example 1: Categorical or numerical?
Warm-up
A survey records each student’s shoe brand, height, blood type and number of siblings. How many of these variables are categorical?
Answer: Two variables are categorical: shoe brand and blood type.
Example 2: Percent in a category
Core
In a survey of 40 students, 14 chose soccer, 10 chose basketball and 16 chose another sport. What percent chose soccer?
Relative frequency: 1440.
1440 = 0.35 = 35%.
Answer: 35% of the students chose soccer.
Example 3: Choosing the right summary
Test-style
A pet store records the type of 25 pets sold: 11 dogs, 8 cats, 4 fish and 2 birds. Which measure of center makes sense, and what percent of the sales does it represent?
Pet type is categorical, so a mean or median of “dog, cat, fish” has no meaning.
The mode is the most common category: dog, with 11.
1125 = 0.44 = 44%.
Answer: Only the mode makes sense: dog, which is 44% of the sales.
Common mistakes
✗ MistakeAveraging number labels: the mean ZIP code of the class is 90{,}210.5.
✓ InsteadZIP codes are categories. Report counts or the most common ZIP code instead.
Numbers that name things are labels, so adding them gives a meaningless result.
✗ MistakeDrawing a histogram (touching bars on a number scale) for favorite colors.
✓ InsteadUse a bar graph with gaps between the bars, in any order you like.
Categories are not points on a number line, so there is no scale for the bars to sit on.
✗ MistakeCalling “number of siblings” categorical because the answers are 0, 1, 2 or 3.
✓ InsteadNumber of siblings is a count, so it is numerical (quantitative).
The test is not how many different answers there are, but whether the values are amounts.
Not to be confused with
Categorical Datavs.Numerical (quantitative) data
Numerical data are counts or measurements, such as height in cm or minutes of homework, so a mean makes sense. Categorical data are labels, such as hair color.
Data are any collected facts or values. Categorical data are one kind, the kind that sorts individuals into groups.
Quick check: 3 questions
Question 1 of 3
Which variable is categorical?
Show answer and explanation
Answer: B. A ZIP code is a label for a place; averaging ZIP codes means nothing. Temperature, age and distance are measurements, so they are numerical.
Question 2 of 3
Which display is a good choice for categorical data such as favorite music genre?
Show answer and explanation
Answer: A. A bar graph shows one bar per category. Histograms and box plots need numbers on a scale, and a scatter plot needs two numerical variables.
Question 3 of 3
Of 30 survey responses, 12 are “yes.” What is the relative frequency of “yes”?
Show answer and explanation
Answer: D.1230 = 0.4 = 40%. 12% treats the count as a percent, 0.4% forgets to multiply by 100, and 60% is the share that did not answer yes.
Categorical Data: frequently asked questions
Is categorical data the same as qualitative data?
Yes. Statistics books use both names for data that place individuals into groups, such as hair color or type of car. The opposite is quantitative (numerical) data, which are counts or measurements. Some books add that ordered categories, such as small, medium and large, are ordinal, and unordered ones are nominal.
Can categorical data be numbers?
Yes. ZIP codes, jersey numbers, phone numbers and student ID numbers are written with digits, but they only name things. A good test: ask whether the mean would make sense. The mean of two jersey numbers tells you nothing, so those numbers are categorical.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 8.SP.A.4, CCSS HSS-ID.B.5
Cite this entry
Effortless Math Team. “Categorical Data.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/categorical-data/
Flashcard
TermCategorical Datalabels, not amounts
DefinitionData that sort individuals into groups, like favorite fruit or blood type. Summarize by counting each category: apple 5, banana 4, grape 3.
Bar GraphA bar graph uses bars to compare amounts in different categories. The taller or longer the bar, the larger the value it represents. Each bar stands for one category, such as a favorite sport, and its length is read against a number scale. Bars can be vertical or horizontal, with gaps between them.Statistics · Grade 3, Grade 4, Grade 5Two-Way TableA two-way table shows counts for two categorical variables collected from the same group, with one variable in the rows and the other in the columns. Each inside cell is a joint frequency, and the totals in the margins are marginal frequencies. Dividing a cell by a row or column total gives relative frequencies that reveal associations.Statistics · Grade 8, Algebra 1NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Relative FrequencyRelative frequency is how often a value or event occurs compared with the total number of observations: frequency ÷ total. It can be a fraction, a decimal or a percent. If 12 of 40 students choose apples, the relative frequency of apples is 1240 = 0.3, or 30%. All the relative frequencies in a table add to 1.Statistics · Grade 7, Grade 8, StatisticsModeThe mode is the value that appears most often in a data set. To find it, count how many times each value occurs and pick the most frequent one. A data set can have one mode, more than one mode, or no mode at all when every value appears only once. The mode works for categories, too.Statistics · Grade 5, Grade 6, Grade 7DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6AverageAn average is one number that stands for the typical size of the values in a data set. In everyday math, average means the mean: add all the values, then divide by how many values there are. In statistics, the median and the mode are also kinds of average.Statistics · Grade 5, Grade 6, Grade 7MedianThe median is the middle value when data are listed in order. If there is an even number of values, the median is the average of the two middle values. Half the data lie at or below the median and half at or above it, and outliers barely move it.Statistics · Grade 5, Grade 6, Grade 7HistogramA histogram uses bars to show how numerical data are grouped into intervals. The data are split into equal-width intervals, called bins, and each bar’s height is the count of values in that interval. The bars touch, because the intervals are continuous, which is what distinguishes a histogram from a bar graph.Statistics · Grade 6, Grade 7, Grade 8HeightHeight is how tall something is: the distance from its bottom to its top, measured straight up and down. In geometry, the height of a shape is the perpendicular distance from a base to the opposite vertex or side, so it always meets the base at a right angle. Area and volume formulas use it.Measurement · Grade 2, Grade 5, Grade 6InchAn inch is a US customary unit of length equal to one twelfth of a foot, about the width of an adult thumb. Its abbreviation is in. Rulers split each inch into halves, quarters, eighths and sixteenths. One inch is exactly 2.54 centimeters, and 12 inches make 1 foot.Measurement · Grade 2, Grade 3, Grade 4Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6StatisticsStatistics is the branch of math that collects, organizes, analyzes and interprets data to answer questions. Descriptive statistics summarize data with graphs and numbers such as the mean and median. Inferential statistics use a sample to draw conclusions about a whole population, with a stated amount of uncertainty.Statistics · Grade 6, Grade 7, Grade 8Joint FrequencyJoint frequency is the number of data values that fit two categories at the same time, such as students who are in Grade 7 and play an instrument. In a two-way table, a joint frequency is one of the inside cells, not the totals. Dividing it by the grand total gives the joint relative frequency.Statistics · Grade 8, Algebra 1