GCSE Maths Practice: relative-frequency

Question 4 of 11

This question uses experimental results to predict outcomes in a larger number of trials.

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\( \begin{array}{l}\text{A spinner is spun 25 times and lands on green} \\ \text{9 times. Estimate how many times it would land on} \\ \text{green in 100 spins.}\end{array} \)

Choose one option:

Use relative frequency as an estimate, then scale it to the new number of trials.

Using Relative Frequency to Make Predictions

At Higher GCSE level, relative frequency is often used not only to describe past results but also to make predictions about future outcomes. This type of question tests whether you can scale up experimental data to estimate what might happen if an experiment is repeated more times.

From Observation to Prediction

Relative frequency is calculated using observed data from an experiment. Once this value is known, it can be used as an estimate of probability. This estimated probability can then be multiplied by a new number of trials to predict how many times an outcome is likely to occur in the future.

General Method

When predicting future outcomes using relative frequency, follow these steps:

  • Calculate the relative frequency from the original experiment.
  • Treat this value as an estimated probability.
  • Multiply the estimated probability by the new number of trials.
  • Interpret the result sensibly, remembering it is only an estimate.

Worked Example 1

A spinner is spun 50 times and lands on blue 14 times. The relative frequency of blue is calculated. This value is then multiplied by 200 to estimate how many times blue would appear in 200 spins.

Worked Example 2

A dice is rolled 40 times and lands on an even number 18 times. The relative frequency of rolling an even number is used to predict how many even numbers might appear in 120 rolls.

Worked Example 3

A survey shows that 27 out of 60 people prefer walking to school. This relative frequency is used to estimate how many people in a group of 300 might prefer walking.

Common Higher-Tier Mistakes

  • Using the theoretical probability instead of the experimental data.
  • Forgetting to scale the relative frequency up to the new number of trials.
  • Assuming the estimate will be exact rather than approximate.
  • Rounding too early and losing accuracy.

Why These Predictions Are Only Estimates

Predictions based on relative frequency are not guarantees. Random variation means that results may differ when the experiment is repeated. However, when experiments involve larger numbers of trials, predictions based on relative frequency are usually more reliable.

Real-Life Applications

This method is widely used in real life. Weather forecasts use past data to predict future conditions, businesses use customer data to estimate demand, and scientists use experimental results to predict future outcomes. In each case, predictions are based on observed trends rather than certainty.

Frequently Asked Questions

Will the prediction always be accurate?
No. It is an estimate based on past data and may differ when the experiment is repeated.

Should I round my final answer?
Only if the question requires it. Otherwise, keep as much accuracy as possible.

Why not use theoretical probability?
Because the question asks you to base your prediction on experimental results, not ideal conditions.

Study Tip

In Higher GCSE probability questions, phrases like "estimate," "predict," or "how many times would you expect" are strong clues that you should use relative frequency and scale it to the new number of trials.

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