View source for Variable (Statistics)

In statistics, a '''variable''' is a characteristic of a subject that varies in a ''non-random'' way.

= Overview and Related Definitions =

At the top level of statistics, we investigate a '''population''': a set of units that we are interested in studying.

Populations are almost always impossible to study due to their massive size and other constraints. Therefore, we take a '''sample''': a subset of the population. 

A '''subject''' is a unit that we study in a population or a sample, and a '''variable''' is a particular characteristic of the subject that we are interested in studying.

= Types of Variables =

There are two types of variables, each with two sub-categories that have useful properties:

* '''Quantitative/Numerical''' variables are measured with numbers. Their sum has meaning.
** '''Continuous''' numerical variables can theoretically take on any number within an interval, whereas
** '''Discrete''' numerical variables have natural gaps
* '''Qualitative/Categorical''' variables are measured as labels. Their sum does not have meaning.
** '''Ordinal''' categorical variables have a natural ordering, whereas
** '''Nominal''' categorical variables do not

It is possible for a categorical variable to be denoted with numbers; a common example would be an ID number. The biggest difference between categorical variables denoted as numbers and numerical variables is the fact that the sum/mean of categorical variables does not have meaning, whereas that of numerical variables do.

= Notation =

A capitalized character (usually <math>X, Y, Z</math>) is used to denote ''all possible values'' of a variable. This is called a '''major'''. When we say "variable", we usually mean this.

A lower case character corresponding to the major is used to denote a specific value of that major (such as <math>x, y, z</math>. This is called a '''statistic'''.

= Random Variable =
A '''random''' variable is a numerical variable whose outcome is the result of a random process (i.e. we don't know what will happen for certain). See [[Random Variable]].
[[Category:Statistics]]