Definition:Relative Frequency

Definition

Let $S$ be a sample or a finite population.

Let $\omega$ be a qualitative variable, or a class interval of a quantitative variable.

The relative frequency of $\omega$ is defined as:

$\map {\operatorname {RF} } \omega := \dfrac {f_\omega} n$

where:

$f_\omega$ is the (absolute) frequency of $\omega$

$n$ is the number of individuals in $S$.

Examples

Arbitrary Example

Consider the sample:

$2, 5, 3, 3, 3, 5, 3, 6, 2, 3, 9, 5$

There are $12$ observations in this sample.

The relative frequency of the observation $3$ is $\dfrac 5 {12}$.

The relative frequency of the observation $9$ is $\dfrac 1 {12}$.

Also see

• Definition:Absolute Frequency

• Definition:Relative Frequency Model for this concept in the context of Probability Theory.

• Results about relative frequency can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): frequency: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): probability
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relative frequency
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): frequency: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): probability
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relative frequency
• 2011: Charles Henry Brase and Corrinne Pellillo Brase: Understandable Statistics (10th ed.): $\S 2.1$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): relative frequency