GCSE Maths Practice: relative-frequency

Relative Frequency from Spinner Experiments

At Higher GCSE level, relative frequency questions often require careful calculation and clear interpretation. When working with spinners, dice, or similar experiments, relative frequency is used to describe how often an outcome occurs based on observed results rather than theoretical expectations.

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 calculated after an experiment has taken place and is based on evidence collected during that experiment. Because it depends on observed data, relative frequency can vary if the experiment is repeated.

Method for Calculating Relative Frequency

The steps for calculating relative frequency are always the same:

• Identify the outcome you are interested in.
• Count how many times this outcome occurred.
• Divide this number by the total number of trials.
• Simplify the fraction or convert it to a decimal if required.

Worked Example 1

A spinner is spun 120 times and lands on blue 31 times. The relative frequency of landing on blue is found by dividing the number of blue outcomes by the total number of spins. The answer can be written as a fraction or decimal.

Worked Example 2

A dice is rolled 150 times and lands on an odd number 67 times. The relative frequency of rolling an odd number is calculated by comparing the number of odd outcomes to the total number of rolls.

Worked Example 3

A survey records how students travel to school over 200 days. Cycling is recorded on 54 days. The relative frequency of cycling to school is found by dividing the number of cycling days by the total number of days observed.

Common Higher-Tier Mistakes

• Dividing by the number of sections on the spinner instead of the number of spins.
• Mixing up theoretical probability with experimental results.
• Failing to simplify fractions when required.
• Rounding too early and losing accuracy.

Why Relative Frequency Matters

Relative frequency is widely used to analyse real data. Scientists use it to evaluate experimental results, businesses use it to understand customer behaviour, and statisticians use it to identify trends. In all cases, conclusions are drawn from observed evidence rather than assumptions.

Fractions and Decimals at Higher Tier

At Higher GCSE level, you may be expected to give your answer as a simplified fraction, a decimal, or sometimes both. Always check the form of the answers given in the question to decide how your final answer should be presented.

Frequently Asked Questions

Can relative frequency change if the experiment is repeated?
Yes. Different runs of the same experiment can produce slightly different results.

Is relative frequency the same as probability?
Relative frequency is an estimate of probability based on observed results.

Should I always simplify?
Yes, unless the question specifically asks for an unsimplified form.

Study Tip

In Higher GCSE probability questions, look carefully at the answer options. If fractions are given, simplify fully. If decimals are given, convert your fraction carefully before choosing an answer.