Data
Statistics & ProbabilityData is a collection of facts, measurements, or observations gathered for analysis.
Definition
Data is information that has been collected. It can be numbers, words, measurements, or observations about the world.
Example
The heights of students in a class ($60$ in, $62$ in, $58$ in, $\ldots$) or the favorite colors students chose (blue, red, blue, green, ...) are both examples of data.
Key Insight
Data is the raw material of statistics. Before you can find patterns or draw conclusions, you need to gather data.
Definition
Data is a collection of values measured or observed on one or more variables. Data can be quantitative (numerical) or qualitative (categorical), and it can come from experiments, surveys, or observational studies.
Example
A weather station records daily high temperatures for a year: that set of $365$ numbers is quantitative data. A survey asking students their favorite school subject produces qualitative (categorical) data.
Key Insight
The type of data determines which statistical methods are appropriate. Numerical data supports means and standard deviations; categorical data calls for frequencies and proportions.
Definition
In formal statistics, 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 $F$. Data structure (univariate, multivariate, time-series, panel) dictates model choice and estimator properties.
Example
Cross-sectional data collects one observation per subject at a single point in time; longitudinal (panel) data tracks the same subjects over time, enabling fixed-effects models that control for unobserved individual heterogeneity.
Key Insight
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.