GCSE Maths Practice: relative-frequency

Question 8 of 11

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

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\( \begin{array}{l}\text{A spinner with 5 equal sections (red, blue, green,} \\ \text{yellow, purple) is spun 50 times. It lands on red} \\ \text{24 times. Estimate how many times it will land on red in 150 spins.}\end{array} \)

Choose one option:

Use experimental results to estimate probability, then scale up to the new number of trials.

Predicting Outcomes Using Relative Frequency

At Higher GCSE level, relative frequency is often used not just to describe past experimental results, but to predict what may happen if the experiment is repeated more times. This type of question tests your ability to use experimental probability and proportional reasoning together.

From Experimental Results to Predictions

Relative frequency is found by dividing the number of times an outcome occurs by the total number of trials. This value acts as an estimate of probability. Once this estimate is known, it can be scaled up to predict how many times the same outcome is likely to occur in a larger number of trials.

General Method

To make predictions 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 40 times and lands on blue 11 times. The relative frequency of blue is calculated and then multiplied by 200 to estimate how many times blue would appear in 200 spins.

Worked Example 2

A dice is rolled 60 times and lands on an even number 29 times. This relative frequency is used to predict how many even numbers might appear in 180 rolls.

Worked Example 3

A survey records that 35 out of 100 students walk to school. This relative frequency is scaled up to estimate how many students in a school of 600 might walk to school.

Common Higher-Tier Mistakes

  • Using theoretical probability instead of experimental data.
  • Forgetting to multiply by the new number of trials.
  • Assuming the prediction will be exact rather than approximate.
  • Rounding too early and reducing accuracy.

Why Predictions Are Only Estimates

Predictions based on relative frequency are not guarantees. Random variation means that actual results may differ when the experiment is repeated. However, predictions become more reliable when the original experiment involves a larger number of trials.

Real-Life Applications

This method is used widely outside the classroom. Businesses use past sales data to estimate future demand, weather forecasters analyse previous conditions to predict future weather, and scientists use experimental data to predict outcomes in further experiments.

Frequently Asked Questions

Should I round my final answer?
Only if the question specifically asks you to. Otherwise, keep the value exact.

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

Does a larger sample improve accuracy?
Yes. Larger samples generally give more reliable estimates.

Study Tip

In Higher GCSE probability questions, phrases such as "estimate," "predict," or "how many times would you expect" indicate that you should calculate relative frequency and then scale it to the new number of trials.

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