**Types of variables**

__Definition:__** **A **variable**
is a characteristic that changes or varies over time and/or for different
individuals or objects under consideration.

Variables
can be classified into one of two categories: **qualitative **or **quantitative**.

__Definition:__** **A **qualitative
variable** measures a quality or characteristic of an object

A
**quantitative variable **measures a
numerical quantity of an object

Qualitative
variables produce data that can be categorized according to similarities or
differences in quality. They are usually called **categorical data**. Variables such as type of car or species of
animal are qualitative.

Quantitative
variables produce **numerical data**.
The numerical value assigned to a quantitative variable is usually denoted by *x*,

e.g. *x* *=*
height of student or *x* = number of
people in a theatre audience.

It
will be noted that there is a difference in the types of numerical values that
quantitative variables can take. The height of a student can take any value
between the smallest height and the largest height of any student measured. If
the smallest height is 1.36m and the largest 2.10m, the value for the height
can take on any value between 1.36m and 2.10m, which is written as _{}. The height is said to be a **continuous **variable. However, the number of people in a theatre
audience can only be positive whole numbers (including zero if there is no-one
in the audience). This is written as _{} In this case, *x* is said to be a **discrete** variable.

** Definition:** A

A
**discrete **variable can only assume a finite,
countable number of values within a prescribed interval