Variable (Statistics): Difference between revisions
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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. | 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 = | = 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'''. | 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'''. | 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]] | [[Category:Statistics]] | ||
Latest revision as of 06:25, 19 March 2024
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 ) 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 . 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.
