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1.2 · Classify variables and types of data

Learn to classify variables and types of data through clear examples and targeted practice.

Athabasca University MATH 215: Introduction to Statistics

Descriptive Statistics

MATH 215 Study Topic 1.2

Statistics begins with information collected about people, objects, or events. Before summarizing that information, identify what was recorded and what kind of values it can take. These choices affect which summaries make sense. For example, a department code may be written with digits, but adding those digits usually tells us nothing useful. This lesson builds a practical classification routine: name the variable, inspect what its values mean, and classify the data accordingly. No calculation is required for this topic; the key skill is careful interpretation.

What you will learn

Distinguish a variable from the values recorded for that variable.
Classify data as categorical or quantitative.
Distinguish nominal and ordinal categories, and discrete and continuous quantities.
Explain why the meaning of a value matters more than whether it is written as a number.

1. Variables, cases, and data values

A variable is a characteristic that is recorded for each member of a group. A member of that group might be a person, a household, a product, or an event. The individual members being described are sometimes called cases or observational units. For example, in a survey of students, each student is a case; program of study and number of courses taken are variables.

A data value is the recorded result for one case on one variable. If a student reports taking four courses, four is that student's value for the variable number of courses. A collection of values for a variable is data. Do not confuse the variable with its values: “travel time to campus” is a variable, while “18 minutes” is one possible value.

A population is the full group a study is meant to describe. A sample is the part of that group from which information is collected. A parameter is a numerical description of a population, while a statistic is a numerical description calculated from a sample. These terms help describe where data come from; they do not change the type of a variable.

First identify the case, then name the variable, then examine its recorded values.
A parameter describes a population; a statistic describes a sample.

2. Categorical and quantitative data

Categorical data place cases into groups or labels. The values tell us which kind or group applies, rather than how much of something there is. Examples include payment method, province of residence, and a response such as satisfied or dissatisfied. A category can be written as a word, a symbol, or even a number; its role is still categorical when it serves as a label.

Quantitative data are numerical values that represent a count or a measurement. They answer questions such as “how many?” or “how much?” Examples include the number of messages received in a day, the mass of a parcel, and the time spent travelling. Arithmetic such as adding or finding an average can be meaningful for quantitative values, though a particular summary must still suit the question.

To classify a value that looks numeric, ask what it represents. A student number such as 40726 identifies a student; it is not a measured amount, so it is categorical. Similarly, postal codes and jersey numbers are labels. By contrast, a count of 12 deliveries is quantitative because it represents how many deliveries occurred.

Categorical values identify groups; quantitative values represent counts or measurements.
Digits do not automatically make a variable quantitative.

3. Subtypes and a reliable classification routine

Nominal data are categorical data with no natural order among their categories. Examples include eye colour, browser type, and country of birth. One category is not inherently higher or lower than another. You may assign codes to nominal categories for record-keeping, but the codes do not create a meaningful ranking.

Ordinal data are categorical data whose categories have a meaningful order. Examples include a service rating of poor, fair, good, or excellent, and clothing sizes such as small, medium, and large. The order is meaningful, but the gaps between adjacent categories are not necessarily equal. A rating of excellent is above good, but that does not establish a fixed numerical difference between them.

Discrete data are quantitative values that arise from counting and take separate, countable values. The number of pets in a household is discrete: a household can have zero, one, or two pets, but not 1.4 pets in an ordinary count. Continuous data are quantitative measurements that can, in principle, take any value within a range, including values between two recorded values. Length, elapsed time, and temperature are examples. Instruments and recording rules may round a measurement, but that does not make the underlying quantity discrete.

Use this routine. First, say what one case is and name the variable. Second, decide whether each value is a group label or a numerical amount. For labels, ask whether the categories have a natural order: no means nominal; yes means ordinal. For numerical amounts, ask whether the variable counts separate items or measures an amount on a scale: counts are discrete; measurements are continuous. State the classification and give a short reason based on what the values mean.

Nominal and ordinal are types of categorical data.
Discrete and continuous are types of quantitative data.
Classify the underlying variable, not only the way its values are displayed.

4. Work through ambiguous cases

Some variables need extra care. A response recorded as “1 = dissatisfied, 2 = neutral, 3 = satisfied” is ordinal categorical data: the digits encode an order, but do not guarantee equal differences between responses. A count of completed courses is quantitative and discrete. A course mark recorded as a percentage is quantitative, even if a reporting system rounds it to a whole number; the classification depends on what the mark measures and how the study defines it.

The distinction between a count and a measurement is about the quantity being recorded, not merely the appearance of the data. A count often has whole-number values, while a measured quantity can have finer precision. If a study records travel time only to the nearest minute, the recorded values may be whole numbers, but travel time remains a measurement and is usually treated as continuous.

A good classification is specific enough to be useful. Rather than writing only “number,” say “quantitative, discrete count.” Rather than writing only “category,” say “categorical, ordinal” when the categories have a meaningful order. If the study description does not make the meaning clear, state what additional information would resolve the classification.

Recorded rounding does not necessarily change a measurement into a count.
Ordered labels remain categorical when their numerical spacing has no established meaning.

A quick map of data types

Broad type	Subtype	What values mean	Example
Categorical	Nominal	Labels with no natural order	Program of study
Categorical	Ordinal	Labels with a meaningful order	Satisfaction rating
Quantitative	Discrete	A count in separate values	Number of courses
Quantitative	Continuous	A measurement that can vary within a range	Study time

Worked example

Classify variables in a student survey

A college survey records each respondent’s student ID, program of study, satisfaction rating (poor, fair, good, excellent), number of courses currently taken, and weekly study time in hours. Classify each variable and explain the reasoning.

Identify the cases
Each respondent is one case. We classify each recorded characteristic separately, rather than trying to give one type to the entire survey.
Classify identifiers and groups
Student ID is categorical, nominal: its digits identify a person but do not measure an amount or rank students. Program of study is also categorical, nominal because the program names have no natural order.
Classify the rating
Satisfaction rating is categorical, ordinal. The categories can be placed in order from poor to excellent, but the differences between neighboring descriptions are not defined as equal amounts.
Classify the numerical values
Number of courses is quantitative and discrete because it counts courses in separate whole-number amounts. Weekly study time is quantitative and continuous because it measures elapsed time and could, in principle, include fractions of an hour.

Answer: Student ID: categorical, nominal. Program of study: categorical, nominal. Satisfaction rating: categorical, ordinal. Number of courses: quantitative, discrete. Weekly study time: quantitative, continuous.

Check: Each classification follows the meaning of the variable: identification, unordered groups, ordered groups, a count, or a measurement.

Common mistakes and how to avoid them

Calling any variable written with digits quantitative.

Correction: Ask whether the digits measure or count something. ID numbers and postal codes are labels, so they are categorical.

Calling ordered rating categories quantitative because they can be numbered.

Correction: A rating scale is ordinal categorical when its order is meaningful but equal spacing between categories has not been established.

Calling every numerical variable continuous.

Correction: Counts such as the number of courses are discrete; measurements such as time are generally continuous.

Assuming rounded measurements are discrete counts.

Correction: Consider what is measured. Recording time to the nearest minute does not change elapsed time into a count.

Lesson summary

A variable is a characteristic recorded for each case; a data value is one recorded result.
Categorical data describe groups or labels. Nominal categories have no natural order; ordinal categories do.
Quantitative data describe counts or measurements. Counts are discrete; measurements are generally continuous.
Decide from the meaning of the values, not merely their format.

Check your understanding

Question 1

A questionnaire records each person's preferred type of music. Which classification fits best?

Categorical, nominal
Categorical, ordinal
Quantitative, discrete
Quantitative, continuous

Show answer and explanation

Categorical, nominal

Music types are group labels with no natural ranking, so the variable is categorical and nominal.

Question 2

A clinic records the number of appointments a patient attended last month. How should this variable be classified?

Categorical, nominal
Categorical, ordinal
Quantitative, discrete
Quantitative, continuous

Show answer and explanation

Quantitative, discrete

The value is a count of appointments. Counts are quantitative and discrete.

Question 3

A delivery service records travel time in minutes, rounded to the nearest whole minute. What is the usual classification of travel time?

Categorical, nominal
Categorical, ordinal
Quantitative, discrete
Quantitative, continuous

Show answer and explanation

Quantitative, continuous

Travel time is a measured amount that could include fractions of a minute. Rounding is a recording choice and does not change the underlying variable into a count.

Key terms

Case: One member, person, object, or event described by the data.
Variable: A characteristic recorded for each case.
Data value: The recorded result for one case on a variable.
Population: The full group a study aims to describe.
Sample: The part of a population from which information is collected.
Parameter: A numerical description of a population.
Statistic: A numerical description calculated from a sample.
Nominal: Categorical data whose groups have no natural order.

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Published by DoAssignment. This AI-assisted lesson follows Athabasca University MATH 215: Introduction to Statistics, study topic 1.2. It is a study resource, not an official curriculum publication.

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