GCSE Maths Practice: relative-frequency

Relative Frequency from Dice Experiments

Relative frequency is a key idea in GCSE Maths probability and is often introduced using simple experiments such as rolling a dice. Instead of predicting what should happen, relative frequency focuses on what actually happens when an experiment is carried out many times. This makes it especially useful when analysing real data.

What Is Relative Frequency?

Relative frequency compares how many times a particular outcome occurs with the total number of trials. It is based entirely on observed results. Because each experiment can produce slightly different outcomes, relative frequency can vary, especially when the number of trials is small.

Method for Calculating Relative Frequency

The steps for calculating relative frequency are always the same:

• Choose 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 appropriate.

Worked Example 1

A dice is rolled 60 times, and the number 2 appears 14 times. The relative frequency of rolling a 2 is found by dividing the number of times 2 appears by the total number of rolls.

Worked Example 2

A spinner with numbers 1 to 4 is spun 80 times. It lands on number 3 a total of 21 times. The relative frequency of landing on 3 is calculated by comparing the number of successful outcomes to the total number of spins.

Worked Example 3

In a board game, a player records the outcome of rolling a dice over 45 turns. They note that an odd number appears 26 times. The relative frequency of rolling an odd number is found by dividing the number of odd outcomes by the total number of turns.

Common Mistakes to Avoid

• Dividing by the number of possible outcomes instead of the number of trials.
• Using theoretical probability instead of observed results.
• Forgetting to simplify fractions when required.
• Confusing relative frequency with probability rules.

Why Relative Frequency Is Important

Relative frequency is widely used in experiments, games, and statistics. In gaming, it can help decide whether a dice or spinner is fair. In science, it supports conclusions based on repeated trials. In everyday life, it helps people make decisions based on past data.

Frequently Asked Questions

Does relative frequency always match expected probability?
No. However, as the number of trials increases, relative frequency often moves closer to the expected probability.

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 required.

Why can relative frequency change?
It changes because each new trial affects the overall proportion of outcomes.

Study Tip

If a GCSE probability question uses words such as "rolled," "observed," "recorded," or "experiment," this is a strong clue that relative frequency should be calculated.