Definition:Binary Variable

Definition

A binary variable is a random variable which can take one of only $2$ values.

It is conventional for the purposes of data analysis to encode such binary variables by use of a random variable which takes the values $0$ and $1$.

Examples

Gender

A record of the gender of a newborn baby will generally be implemented as a binary variable.

Hence, for example, male may be encoded as $0$, and female as $1$.

Presence or Absence

The presence or absence of a bacterium in a clinical sample be implemented as a binary variable.

Hence, for example, absent may be encoded as $0$, and present as $1$.

Bernoulli Trial

The outcome of a Bernoulli trial may be implemented as a binary variable.

Hence, for example, the outcome from a coin-tossing exercise: heads may be encoded as $0$, and tails as $1$.

Also see

• Definition:Dummy Variable
• Definition:Bernoulli Trial

• Results about binary variables can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): binary variable
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): binary variable