Data Types and Distributions

Written and curated by Emily Potts, MS, Weija Fan, MS, and Caleb Miles, PhD.

Overview

An essential first step of handling data is to determine a variable’s data type. The main data types are numerical and categorical, the latter of which do not exactly correspond to numbers, but rather categories. Numerical variables can be discrete (e.g., taking the values of integers, such as household size) or continuous (i.e., they fall on a continuum, as with age or weight). Categorical variables can be ordinal (not numeric, but having an ordering, e.g., Likert scale survey responses) or nominal (having no natural ordering, e.g., marital status). In statistics, we model variables as being random, and every random variable has a distribution, which determines how frequently different values of the variable occur. A statistical model is a family of distributions that are all the same apart from key identifying quantities known as a parameters. Parameters determine the characteristics of the distribution, such as its center, spread, or shape. For example, the normal distribution has two parameters: one determining its mean (center) and the other its variance (spread). Distribution types correspond to data types; for continuous random variables, there are continuous distributions (e.g., normal, exponential), and for discrete random variables, there are discrete distributions (e.g., binomial, Poisson). Distributions are extremely useful for modeling data. One of the central goals of statistics is to learn (i.e., estimate) the values of the parameters in a statistical model, which can provide essential information about the variables of interest and their relationships to one another.