GCSE Maths Practice: relative-frequency

Question 8 of 10

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

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\( \begin{array}{l}\text{A coin is flipped 50 times and lands heads 30 times.} \\ \text{What is the relative frequency of heads?}\end{array} \)

Choose one option:

Relative frequency always depends on observed outcomes, not on what you expect to happen.

Relative Frequency and Experimental Results

Relative frequency is a core topic in GCSE Maths probability and is used to describe how often an outcome occurs based on real observations. Unlike theoretical probability, which predicts what should happen, relative frequency is calculated after an experiment has taken place and is based entirely on recorded results.

What Is Relative Frequency?

Relative frequency compares the number of times a particular outcome happens to the total number of trials. Because it relies on observation, its value can change as more trials are carried out. Over time, and with more data, the relative frequency often becomes more stable.

Steps to Calculate Relative Frequency

The method for finding relative frequency is always the same:

  • 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 possible.

Worked Example 1

A spinner is spun 70 times and lands on yellow 26 times. The relative frequency of landing on yellow is found by dividing the number of yellow outcomes by the total number of spins.

Worked Example 2

A survey records how 120 people travel to work, and 48 of them walk. The relative frequency of walking to work is calculated by comparing the number of people who walk to the total number surveyed.

Worked Example 3

A student observes the number of days they revise over a 20-day period and records revising on 11 days. The relative frequency of revising is found by dividing the number of revision days by the total days observed.

Common Mistakes to Avoid

  • Dividing by the number of possible outcomes instead of the number of trials.
  • Using expected probability instead of observed data.
  • Leaving fractions unsimplified when simplification is required.
  • Mixing up relative frequency and theoretical probability.

Why Relative Frequency Is Important

Relative frequency is used in many real-life situations. Scientists analyse experimental results, sports analysts track performance over time, and businesses study customer behaviour to predict trends. In all these cases, decisions are based on evidence rather than assumptions.

Frequently Asked Questions

Does relative frequency always stay the same?
No. Relative frequency can change as more trials are added, especially when the sample size is small.

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

Is relative frequency the same as probability?
Relative frequency is an estimate of probability based on observed results, not a guaranteed value.

Study Tip

In GCSE questions, words like "experiment", "observed", "recorded", or "trial" are strong clues that you should calculate relative frequency rather than theoretical probability.

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