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KS3 Bitesize

Maths

Relative frequency

When you toss a coin, there is an equal chance of obtaining a head or a tail. When you throw a die, the probability of getting a 6 is 1/6.

But what is the probability that when you look out of a window at a street, the next car that passes will be red? You can no longer use equally likely outcomes for this. You need to use relative frequency.

Introduction

This Revision Bite covers:

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.

Questions

Try out these example questions about relative frequency.

Question

Q1. 100 people were asked whether they were left-handed. Four people answered 'yes'. What is the relative frequency of 'left-handed'?

Q2. A white counter was taken from a bag of different coloured counters, and then replaced. The relative frequency of getting a white counter was found to be 0.3. If the bag contained 20 counters, estimate the number of white counters.

Answer

A1. The relative frequency is 4/100 = 1/25 or 0.04

A2. The relative frequency of white counters is 0.3, and there are 20 counters in the bag, so, as an estimate, 0.3 × 20 = 6 white counters.

Relative frequency can only be used as an estimate.

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