GCSE Maths Practice: relative-frequency

Question 3 of 11

This question uses experimental results to calculate relative frequency as a decimal.

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\( \begin{array}{l}\text{A fair die is rolled 250 times and lands on the} \\ \text{number 5 exactly 45 times. What is the relative} \\ \text{frequency of rolling a 5?}\end{array} \)

Choose one option:

At Higher tier, relative frequency questions usually expect answers in decimal form.

Relative Frequency as an Estimate of Probability

At Higher GCSE level, relative frequency is often used not just as a calculation, but as a way of estimating probability from real experimental data. Rather than assuming outcomes are perfectly fair, we use observed results to make informed estimates about how likely an event is to occur.

What Is Relative Frequency?

Relative frequency measures how often a particular outcome occurs compared to the total number of trials. It is calculated after an experiment has taken place and is therefore based on evidence rather than theory. Because it depends on observed data, relative frequency can vary from one experiment to another.

Method for Calculating Relative Frequency

The process is always the same:

  • Identify the outcome of interest.
  • Count how many times this outcome occurs.
  • Divide by the total number of trials.
  • Write the result as a decimal when estimating probability.

Worked Example 1

A spinner is spun 400 times and lands on red 76 times. The relative frequency of landing on red is found by dividing the number of red outcomes by the total number of spins and writing the answer as a decimal.

Worked Example 2

A machine produces bolts, and quality control tests 1,000 bolts. If 27 bolts are faulty, the relative frequency of a faulty bolt is calculated and used to estimate the probability that a randomly selected bolt is faulty.

Worked Example 3

A basketball player takes 180 shots in training and scores 61 times. The relative frequency of scoring is used to estimate the probability that the player will score the next shot.

Common Higher-Tier Mistakes

  • Leaving the answer as a fraction instead of a decimal.
  • Confusing relative frequency with theoretical probability.
  • Using the expected probability rather than the observed data.
  • Rounding too early during calculations.

Why Large Numbers of Trials Matter

When experiments involve only a small number of trials, results can fluctuate widely due to chance. As the number of trials increases, these random effects tend to balance out, and the relative frequency becomes a more reliable estimate of the true probability. This idea underpins many areas of statistics, science, and data analysis.

Frequently Asked Questions

Is relative frequency the same as probability?
No. Relative frequency is an estimate of probability based on observed results.

Should I always use a decimal at Higher tier?
Yes, especially when the question asks for a probability estimate or provides decimal answer options.

Can relative frequency change if the experiment is repeated?
Yes. Different runs of the same experiment can produce slightly different results.

Study Tip

In Higher GCSE questions, words such as "estimate", "based on these results", or "experimental probability" are strong clues that you should calculate relative frequency and express it as a decimal.

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