GCSE Maths Practice: relative-frequency

Question 10 of 11

This question uses experimental data to estimate outcomes over a larger number of trials.

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\( \begin{array}{l}\text{In an experiment, a red section was landed on 12} \\ \text{times out of 25 spins. Estimate how many times it} \\ \text{would land on red in 100 spins.}\end{array} \)

Choose one option:

Use experimental results as an estimate, then scale them proportionally.

Estimating Future Outcomes Using Relative Frequency

At Higher GCSE level, relative frequency is often used to move beyond simple calculation and into prediction. Instead of only describing what has already happened, you are asked to use experimental data to estimate what might happen if the experiment were repeated on a larger scale. This skill combines probability with proportional reasoning.

What Relative Frequency Represents

Relative frequency measures how often a particular outcome occurs compared to the total number of trials. Because it is based on observed data, it provides an experimental estimate of probability. This estimate can then be used to predict future outcomes, especially when theoretical probability may not reflect real behaviour.

General Method for Making Predictions

When using relative frequency to predict outcomes in a larger number of trials, follow these steps:

  • Calculate the relative frequency from the original experiment.
  • Use this value as an estimated probability.
  • Multiply the estimated probability by the new number of trials.
  • Interpret the result as an estimate, not an exact value.

Worked Example 1

A spinner is spun 40 times and lands on blue 17 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 odd number 31 times. The relative frequency of rolling an odd number is used to estimate how many odd numbers might appear in 300 rolls.

Worked Example 3

A survey shows that 22 out of 50 people prefer tea to coffee. This relative frequency is scaled up to estimate how many people in a group of 400 might prefer tea.

Why This Is an Estimate, Not a Guarantee

Predictions based on relative frequency are not exact. Random variation means that results can change when an experiment is repeated. However, relative frequency still provides a reasonable estimate, especially when the number of trials is large.

Common Higher-Tier Errors

  • Using theoretical probability instead of experimental results.
  • Forgetting to multiply by the new number of trials.
  • Assuming the estimate will be exact.
  • Rounding too early and losing accuracy.

Why Experimental Probability Is Useful

In many real-life situations, objects are not perfectly fair, or the probability is unknown. In these cases, experimental probability gives a better picture of what is likely to happen. This approach is widely used in science, economics, sports analysis, and quality control.

Frequently Asked Questions

Should I always use relative frequency for predictions?
Yes, when the question tells you to base your answer on experimental results.

Does a larger original sample help?
Yes. Larger samples usually give more reliable estimates.

Why not just repeat the experiment?
Repeating experiments is ideal, but predictions are often needed before more data is available.

Study Tip

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

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