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Relative frequency

Relative frequency

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Explainer Video

Tutor: Alice

Summary

​

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

absolute  frequencynumber  of  trials=relative  frequency\dfrac{\text{absolute \ frequency}}{\text{number \ of \ trials}} = \text{relative \ frequency}number  of  trialsabsolute  frequency​=relative  frequency​​



Example

Andre is testing a 333​-sided spinner, with sides AAA​, BBB​ and CCC​. Using data already in the table, calculate the relative frequency of each outcome.


Outcome

Absolute Frequency

​ AAA​​
​ 666​​
​ BBB​​
​ 101010​​
​ CCC​​
​ 444​​


The total number of trials is 6+10+4=206 + 10 + 4 = 206+10+4=20.


The relative frequency of outcome AAA​ is 620=310‾\dfrac{6}{20} = \underline{\dfrac{3}{10}}206​=103​​.


The relative frequency of outcome BBB​ is 1020=12‾\dfrac{10}{20} = \underline{\dfrac{1}{2}}2010​=21​​.


The relative frequency of outcome CCC​ is 420=15‾\dfrac{4}{20} = \underline{\dfrac{1}{5}}204​=51​​.


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Calculating probability

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Relative frequency

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FAQs - Frequently Asked Questions

Why do relative frequencies sum to 1?

The relative frequencies are estimates of the probabilities and so as the probabilities of outcomes of an experiment sum to 1, so do the relative frequencies.

How are relative frequencies related to probabilities?

The greater the number of trials of an experiment, the more reliable the relative frequency is as an estimate of the probability.

What is frequency?

Frequency is a measure of how often an event has occurred.

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