GCSE Maths Practice: relative-frequency

Relative Frequency in GCSE Probability

Relative frequency is an essential concept in GCSE Maths probability. It is used to describe how often a particular outcome occurs based on observed results rather than theoretical expectations. This makes it especially useful when dealing with experiments, surveys, and real-life data.

Understanding Relative Frequency

Relative frequency compares the number of times a specific outcome happens with the total number of trials. Because it relies on observation, the value can change as more trials are carried out. However, with a larger number of trials, the relative frequency often becomes more stable.

Method for Calculating Relative Frequency

To calculate relative frequency, follow these 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 appropriate.

Worked Example 1

A spinner is spun 60 times and lands on green 21 times. The relative frequency of landing on green is found by dividing the number of green results by the total number of spins. The fraction may then be simplified.

Worked Example 2

A basketball player takes 45 shots during practice and scores 18 times. The relative frequency of scoring is calculated by comparing the number of successful shots to the total number attempted.

Worked Example 3

A student records how many days they walk to school over a 30-day period and notes that they walk on 12 days. The relative frequency of walking to school is found by dividing the number of walking days by the total days recorded.

Common Mistakes to Avoid

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

Why Relative Frequency Is Useful

Relative frequency is widely used in everyday life. Scientists rely on repeated experiments to draw conclusions, sports analysts use data to assess performance, and businesses use customer data to predict future behaviour. In each case, decisions are based on evidence rather than assumptions.

Frequently Asked Questions

Does relative frequency always equal probability?
No. Relative frequency is an estimate of probability based on observed results and can vary from experiment to experiment.

Can relative frequency be written as a decimal or percentage?
Yes. Once calculated, relative frequency can be expressed as a fraction, decimal, or percentage.

Why does relative frequency change?
It changes because new trials can affect the overall proportion of outcomes.

Study Tip

If a GCSE question mentions words such as "experiment", "observed", "recorded", or "trial", it is a strong clue that relative frequency should be used rather than theoretical probability.