### Variables

#### Variable

##### Definition

A variable (usually denoted by letters or symbols) is a characteristic, number, or quantity that takes different values in different situations.

#### Random Variable

##### Definitions

A random variable is a variable which takes any value at random from all of the possible outcomes of an experiment. There are two types of random variable, discrete and continuous.

Note: A non-random variable is a variable which is not random.

#### Types of Variable

The main types of variables include: independent, dependent, qualitative, quantitative, discrete and continuous.

Independent Variable

Dependent Variable

Definition

A variable is independent if it may vary freely and does not depend upon changes in other variables. It is usually denoted by $x$.

A variable is dependent if it varies according to changes in other variables. It is usually denoted by $y$.

Example

Time spent revising for an exam.

The marks from an exam.

Example

How many spoonfuls of sugar you put in your tea.

Qualitative Variable

Quantitative Variable

Definition

A variable is qualitative if it can not be represented by a number.

A variable is quantitative if it can be represented by a number.

Example

The head of department's hair colour.

The number of lecturers with brown hair.

Example

How students travel to university.

The number of students that walk to university.

Discrete Variable

Continuous Variable

Definition

A variable is discrete if it may take only a countable number of distinct values such as $0$, $1$, $2$, $3$, $4$, $\ldots$ If a variable can take only a finite number of distinct values, then it must be discrete.

A variable is continuous if it can take any value within a finite or infinite interval.

Example

The number of people in your family.

The combined weight of your family.

Example

The number of students on your course. 