GCSE Maths Practice: relative-frequency

Question 5 of 10

This question focuses on finding relative frequency using results from repeated coin flips.

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\( \begin{array}{l}\text{A coin is flipped 100 times, and it lands heads 65 times.} \\ \text{What is the relative frequency of heads?}\end{array} \)

Choose one option:

Relative frequency always depends on observed outcomes, not expectations.

Relative Frequency and Experimental Probability

Relative frequency is a core idea in GCSE Maths probability and is closely linked to experimental probability. Instead of predicting what should happen, relative frequency looks at what actually happened during repeated trials. This makes it extremely useful when analysing real data, such as results from experiments, surveys, or repeated observations.

What Does Relative Frequency Tell Us?

Relative frequency shows how often a particular outcome occurs compared to the total number of attempts. It is based entirely on observed results. Because of this, relative frequency can vary from experiment to experiment, especially when the number of trials is small.

How to Calculate Relative Frequency

The calculation method is always the same, regardless of the context:

  • Decide which 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 spinner is spun 50 times. It lands on blue 21 times. The relative frequency of landing on blue is found by dividing the number of blue outcomes by the total number of spins. This gives a fraction that may be simplified.

Worked Example 2

A football player takes 80 penalty shots during training and scores 46 goals. The relative frequency of scoring a penalty is calculated by comparing the number of goals scored to the total number of attempts.

Worked Example 3

A student records how many days it rains over a 40-day period and observes rain on 17 days. The relative frequency of a rainy day is found by dividing the number of rainy days by the total number of days observed.

Common Mistakes Students Make

  • Dividing by the number of possible outcomes instead of the number of trials.
  • Using expected probability instead of observed results.
  • Forgetting to simplify fractions where required.
  • Mixing up relative frequency with theoretical probability.

Why Relative Frequency Is Useful

Relative frequency plays an important role in real life. Scientists rely on repeated experiments to identify patterns, sports analysts use performance data to predict outcomes, and weather forecasters study past data to estimate future conditions. In each case, decisions are made based on observed evidence rather than assumptions.

Frequently Asked Questions

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

Can relative frequency change?
Yes. Adding more trials can change the relative frequency, especially when the sample size is small.

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

Study Tip

If a GCSE probability question mentions words such as experiment, observed, recorded, or trial, it is a strong sign that relative frequency should be used instead of theoretical probability.

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