Data
Data is a collection of facts, measurements, or observations gathered for analysis.
Definition
Data is information that has been collected: numbers, words, measurements, or observations about the world, gathered on one or more variables from experiments, surveys, or observational studies. It can be quantitative (numerical) or qualitative (categorical). Formally, data is a realized sample from a probability space, a set of observations $\{x_1, x_2, \ldots, x_n\}$ drawn from a population distribution $F$, and its structure (univariate, multivariate, time-series, panel) dictates which models and estimators are appropriate.
Example
The heights of students in a class ($60$ in, $62$ in, $58$ in, $\ldots$) are quantitative data, while the favorite colors students chose (blue, red, blue, green, ...) are qualitative data. A weather station recording daily high temperatures for a year produces $365$ quantitative values, while a survey asking students their favorite school subject produces qualitative data. Cross-sectional data collects one observation per subject at a single point in time, while longitudinal (panel) data tracks the same subjects over time, enabling fixed-effects models that control for unobserved individual heterogeneity.
Key Insight
Data is the raw material of statistics: before you can find patterns or draw conclusions, you need to gather it, and the type of data determines which statistical methods are appropriate (numerical data supports means and standard deviations, categorical data calls for frequencies and proportions). The phrase "data generating process" (DGP) captures the idea that observed data is one realization of a stochastic mechanism; identifying the DGP correctly is essential for valid inference.