**

# Relative frequency

## In a nutshell

After running an experiment, you can use the data collected to calculate relative frequencies. You can then use these relative frequencies to estimate probabilities of events from the experiment.

## Random event

### Definition

A random event is an event whose outcome depends on chance, for instance flipping a coin or rolling a die.

## Absolute and relative frequency

### Absolute frequency

This is the number of times a certain event has occurred.

### Relative frequency

The relative frequency of an event is the proportion of the number of times the event has occurred compared to the total number of trials. This allows you to compare two situations where a different number of trials has been used in each.

### Formula

$\dfrac{\text{absolute \ frequency}}{\text{number \ of \ trials}} = \text{relative \ frequency}$

##### Example

*Andre is testing a $3$-sided spinner, with sides $A$, $B$ and $C$. Using data already in the table, calculate the relative frequency of each outcome.*

#### Outcome | #### Absolute Frequency |

$A$ | $6$ |

$B$ | $10$ |

$C$ | $4$ |

*The total number of trials is $6 + 10 + 4 = 20$.*

*The relative frequency of outcome $A$ is $\dfrac{6}{20} = \underline{\dfrac{3}{10}}$*.

*The relative frequency of outcome $B$ is $\dfrac{10}{20} = \underline{\dfrac{1}{2}}$*.

*The relative frequency of outcome $C$ is $\dfrac{4}{20} = \underline{\dfrac{1}{5}}$*.