Types of Data

Precise definition

Categorical data record group membership; nominal categories have no intrinsic order, while ordinal categories do. Quantitative data record numerical magnitude; discrete variables take countable values and continuous variables can vary over intervals within measurement precision.

Notation and mathematical language

Interval scales have meaningful differences but no meaningful absolute zero, while ratio scales support meaningful ratios because zero represents absence of the quantity. These labels guide permissible summaries, but subject-matter meaning matters more than storage type.

Conceptual picture

Numbers can be labels, ranks, counts, or measurements. The operation must preserve meaning: a median can summarize ordered categories, while a mean of arbitrary nominal codes cannot. Continuous measurements are stored discretely after rounding but remain conceptually continuous.

Fully worked example

Interpretation and application

Correct type classification prevents meaningless averages, inappropriate charts, and invalid models in surveys, experiments, and databases. It does not by itself address bias, dependence, or causation.

Common mistakes