Data and Variables

A rigorous introduction to observational units, variables, datasets, coding, and the limits of measurement.

A variable records one characteristic; its type determines which summaries make sense. A set of observations branches into categorical and quantitative variables, with quantitative values divided into discrete and continuous examples. Small chart icons show that the representation follows the variable type.

Precise definition

A dataset records values of one or more variables on observational units. A variable is a characteristic that can differ among units. An explanatory variable is used to explain or predict; a response is the outcome of interest. These roles come from the research question, not from a column's numeric format.

Notation and mathematical language

An observation is typically one row and a variable one column in tidy rectangular data, though repeated or hierarchical measurements require identifiers and structure. Population parameters summarize a population; sample statistics summarize observed data and estimate parameters under a sampling model.

Conceptual picture

Measurement turns concepts into recorded values. Coding categories with numbers does not make them quantitative; identifiers such as postal codes support matching rather than arithmetic. Metadata document units, missing-value codes, definitions, and collection timing.

Fully worked example

Interpretation and application

Clear variable definitions prevent errors in health records, surveys, experiments, and business analytics. A technically correct computation on misidentified units can answer a different question with unwarranted precision.