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Relative frequency

Relative frequency

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Proportion


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Explainer Video

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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}​​



Example

Andre is testing a 33​-sided spinner, with sides AA​, BB​ and CC​. Using data already in the table, calculate the relative frequency of each outcome.


Outcome

Absolute Frequency

AA​​
66​​
BB​​
1010​​
CC​​
44​​


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


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


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


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


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Exercises

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FAQs - Frequently Asked Questions

Why do relative frequencies sum to 1?

How are relative frequencies related to probabilities?

What is frequency?

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