GCSE Maths Practice: relative-frequency

Question 4 of 10

This question focuses on finding relative frequency using observed data from repeated trials.

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\( \begin{array}{l}\text{A bag contains 5 red and 3 blue marbles.} \\ \text{The bag is shaken 40 times, and a red marble is drawn 20 times.} \\ \text{What is the relative frequency of drawing a red marble?}\end{array} \)

Choose one option:

Relative frequency is based on what actually happened, not what you expect to happen.

Relative Frequency in Probability

Relative frequency is a fundamental concept in GCSE Maths probability. Unlike theoretical probability, which is based on what should happen, relative frequency is based on what actually happens when an experiment is carried out multiple times. This makes it especially useful when working with real data collected from observations, experiments, or repeated trials.

What Is Relative Frequency?

Relative frequency measures how often a specific outcome occurs compared to the total number of attempts. It is calculated after an experiment has taken place and uses recorded results rather than predictions. Because it is based on evidence, relative frequency is commonly used in statistics, science, sports analysis, and everyday decision-making.

How to Calculate Relative Frequency

The process for finding relative frequency always follows the same steps:

  • Identify the outcome you are interested in.
  • Count how many times this outcome occurs.
  • Divide this number by the total number of trials.
  • Simplify the fraction if possible.

Worked Example 1

A spinner is spun 24 times. It lands on green 9 times. The relative frequency of landing on green is found by dividing the number of green outcomes by the total number of spins. The resulting fraction may then be simplified.

Worked Example 2

A basketball player takes 50 free throws and successfully scores 22 times. The relative frequency of scoring a free throw is calculated by comparing the number of successful shots to the total number attempted.

Worked Example 3

A weather station records sunshine over 30 days and observes sunshine on 14 days. The relative frequency of a sunny day is found by dividing the number of sunny days by the total number of days observed.

Common Mistakes to Avoid

  • Dividing by the number of possible outcomes instead of the number of trials.
  • Using the contents of a bag rather than the observed results.
  • Confusing relative frequency with theoretical probability.
  • Leaving the answer unsimplified when simplification is required.

Why Relative Frequency Is Important

Relative frequency is widely used in real-life situations. Scientists use it to analyse experimental results, sports analysts rely on it to track performance trends, and businesses use past customer data to predict future behaviour. In all these cases, conclusions are drawn from observed evidence rather than assumptions.

Frequently Asked Questions

Does relative frequency change over time?
Yes. As more trials are carried out, relative frequency can change and usually becomes more stable.

Can relative frequency be written as a decimal or percentage?
Yes. Once the fraction is found, it can be converted into a decimal or percentage if needed.

Is relative frequency always accurate?
It is an estimate based on observations. Larger sample sizes generally lead to more reliable results.

Study Tip

Look out for words such as observed, recorded, experiment, or repeated in GCSE questions. These are strong clues that the question is testing relative frequency rather than theoretical probability.

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