GCSE Maths Practice: relative-frequency

Relative Frequency Using Dice Experiments

Relative frequency is an important idea in GCSE Maths probability because it allows us to describe how often an event occurs based on real observations. When working with experiments such as rolling a dice, relative frequency helps us analyse results that have already happened rather than predicting what should happen.

What Is Relative Frequency?

Relative frequency compares the number of times a specific outcome occurs to the total number of trials. It is calculated after an experiment has been completed and uses recorded data. Because it depends on observations, the value can change as more trials are carried out.

How to Calculate Relative Frequency

The method for calculating relative frequency is always the same, no matter the experiment:

• 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 5 appears 11 times. The relative frequency of rolling a 5 is found by dividing the number of times 5 appears by the total number of rolls.

Worked Example 2

A spinner with numbered sections is spun 80 times. The spinner lands on the number 2 a total of 19 times. The relative frequency of landing on 2 is calculated by comparing the number of successful outcomes to the total number of spins.

Worked Example 3

A board game requires players to roll a dice. Over 45 turns, a player records rolling an even number 26 times. The relative frequency of rolling an even number is found by dividing the number of even outcomes by the total number of turns.

Common Mistakes to Avoid

• Dividing by the number of possible outcomes instead of the number of rolls.
• Using theoretical probability rather than observed results.
• Forgetting to simplify fractions where needed.
• Confusing relative frequency with probability rules.

Why Relative Frequency Is Useful

Relative frequency is widely used in games, experiments, and data analysis. In gaming, it helps assess fairness; in science, it supports conclusions based on repeated trials; and in statistics, it helps identify patterns. The more trials that are recorded, the more reliable the conclusions usually become.

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 in different forms?
Yes. It can be written as a fraction, decimal, or percentage depending on the question.

Why does 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.