GCSE MATHS • HIGHER TIER
Relative Frequency Made Simple
Estimate probability from experimental results and use observed data to make predictions.
Clear method
Exam practice
Worked proofs
Relative Frequency in Four Moves
1
Observe
Identify how many times the event occurred.
2
Count
Identify the total number of trials.
3
Divide
Divide the number of event occurrences by the total number of trials.
4
Predict
Use the relative frequency to estimate future outcomes when required.
What You’ll Learn
Understand relative frequency as an estimate of probability.
Use the relative frequency formula.
Calculate relative frequency from experimental data.
Use relative frequency to predict future outcomes.
Understand the link with experimental probability.
Apply relative frequency to real-life data.
Key Rules
Relative frequency is an estimate of probability based on observed results.
Use the formula :
Relative frequency = Number of times the event occurs ÷ Total number of trials.
The number of successful outcomes goes on top.
The total number of trials goes underneath.
Relative frequency must be between 0 and 1.
Worked Proof: Relative Frequency
Step-by-Step Method
- 1. Identify how many times the event occurred.
- 2. Identify the total number of trials.
- 3. Divide the event occurrences by the total trials.
- 4. Simplify or convert the answer if required.
- 5. Multiply by the future number of trials when making a prediction.
- 6. Check that the relative frequency is between 0 and 1.
More Worked Examples
1
Question: A coin is tossed 100 times and lands on heads 56 times. Find the relative frequency of heads.
Relative Frequency = 56 ÷ 100
= 0.56
2
Question: A dice is rolled 120 times and a six appears 18 times.
Relative Frequency = 18 ÷ 120
= 0.15
3
Question: A spinner lands on red 35 times in 50 spins.
Relative Frequency = 35 ÷ 50
= 0.70
4
Question: A football team wins 24 matches out of 40
Relative Frequency = 24 ÷ 40
= 0.60
- Common GCSE Mistakes
- Dividing in the wrong order.
- Forgetting that relative frequency is only an estimate.
- Using relative frequency incorrectly when making predictions.
- Exam Tips
- Put the number of successful outcomes on top and total trials underneath.
- Check that your relative frequency is between 0 and 1.
- Remember that relative frequency is based on observed results.
- For predictions, multiply the relative frequency by the new number of trials.
- Do not confuse experimental probability with theoretical probability.
- Show the division clearly before giving your decimal answer.
Skills Used in Relative Frequency
Relative Frequency
Experimental Probability
Division
Decimals
Fractions
Percentages
Prediction
Data Handling
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Frequently Asked Questions
Relative frequency is an estimate of probability based on the observed results of an experiment.
Relative Frequency = Number of times the event occurs ÷ Total number of trials.
No. Relative frequency uses actual observations, while theoretical probability is based on what should happen.
Multiply the relative frequency by the number of future trials to estimate how many times the event may occur.
It is based on actual experimental observations rather than theoretical calculations.
The source explains that relative frequency often gets closer to the theoretical probability.