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Maths

Relative frequency

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Estimating probability

For an experiment or survey:

Relative frequency = number of times the event happens ÷ total number of trials

For example, if you observed 100 passing cars and found that 23 of them were red, the relative frequency is 23/100.

Accuracy

In the Probability Revision Bite, you learnt that you get a more accurate result in surveys of events if you carry out a large number of trials or survey a large number of people.

Example

A bag of sweets containing 3 red sweets and 7 blue sweets

A bag contains 3 red sweets and 7 blue sweets.

Tom took a sweet from the bag, noted its colour and then replaced it.

He did this 10 times and found that he obtained a red sweet on 4 occasions (ie the relative frequency was 4/10).

He then carried out the experiment another 10 times, combined his results with the first trial and saw that - in total - he had obtained a red sweet on 5 out of 20 occasions (ie the relative frequency was 5/20 ).

Tom continued in this way, recording his combined results after every 10 trials and showing them on the graph below:

Graph showing relative frequency. After 10 trials the frequency is 0.4; after 20 trials the frequency is 0.25; after 30 trials the frequency is 3.5; after 50 trials the frequency is 0.19; after 60 trials the frequency is 0.28; after 70 trials the frequency is 0.32; after 80 trials the frequency is 0.25; after 90 trials the frequency is 0.35; after 100 trials the frequency is 0.28. The overall relative frequency is 0.3

We can see from the graph that relative frequency gets better (ie closer to the true probability) as the number of trials increases.

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