GCSE Maths Practice: relative-frequency

Relative Frequency in Dice Experiments

Relative frequency is a key concept in GCSE Maths probability and is commonly introduced through simple experiments such as rolling a die. Instead of predicting outcomes in advance, relative frequency focuses on analysing what actually happens when an experiment is repeated many times. This makes it especially useful when working with real data.

What Is Relative Frequency?

Relative frequency compares the number of times a particular outcome occurs with the total number of trials carried out. It is always based on observed results rather than expectations. Because of this, relative frequency can change as more trials are added, particularly when the sample size is small.

Steps to Calculate Relative Frequency

The method for calculating relative frequency is always the same:

• 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 die is rolled 80 times and the number 2 appears 19 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 labelled 1 to 5 is spun 60 times. It lands on number 5 a total of 14 times. The relative frequency of landing on 5 is calculated by comparing the number of successful outcomes to the total number of spins.

Worked Example 3

In a classroom experiment, students roll a die 45 times and record rolling an even number 27 times. The relative frequency of rolling an even number is found by dividing the number of even outcomes by the total number of trials.

Common Mistakes to Avoid

• Dividing by the number of possible outcomes instead of the number of trials.
• Using theoretical probability rather than observed results.
• Leaving fractions unsimplified when simplification is required.
• Mixing up relative frequency with probability rules.

Why Relative Frequency Is Important

Relative frequency is widely used in experiments, games, and statistics. It helps determine whether a die or spinner behaves fairly and supports conclusions based on real data. In science and everyday decision-making, relative frequency provides evidence-based insight rather than assumptions.

Frequently Asked Questions

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

Can relative frequency be written as a decimal or percentage?
Yes. After finding the fraction, it can be converted into a decimal or percentage if required.

Why can relative frequency change?
Because each additional trial can affect the overall proportion of outcomes.

Study Tip

If a GCSE probability question includes words such as "rolled", "observed", "recorded", or "experiment", this is a strong clue that you should calculate relative frequency rather than theoretical probability.