Skip to content
VirtusAcademy

Relative Frequency

FoundationHigherAQAEdexcelOCR

Get to grips with relative frequency using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on using relative frequency to estimate probability, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Relative frequency = successes ÷ total trials.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Relative frequency estimates a probability from experimental results rather than from theory. It is the number of times an event occurred divided by the number of trials.

So if a drawing pin lands point-up \(37\) times in \(100\) drops, the relative frequency is \(0.37\). This is an estimate of the true probability, which cannot be calculated theoretically for an irregular object.

The estimate improves as the number of trials increases. With few trials the relative frequency fluctuates considerably, but over many trials it settles close to the true probability.

Revision notes

Calculating relative frequency

Divide the number of successes by the number of trials.

If a spinner lands on red \(24\) times in \(80\) spins, the relative frequency is \(24 \div 80 = 0.3\).

Estimating expected outcomes

Multiply the probability by the number of trials to predict how often an event will occur.

With a probability of \(0.3\) over \(200\) spins, you would expect about \(60\) reds. The word expect matters — the actual result will vary.

Judging fairness

Compare the relative frequency with the theoretical probability.

If a fair dice should give \(\frac{1}{6}\) but a six appears in \(40\%\) of many trials, the dice is probably biased. A small difference over few trials proves nothing.

Key points

  • Relative frequency estimates probability from experiments.
  • It is successes divided by trials.
  • It improves with more trials.
  • Expected outcomes are probability times trials.
  • Compare with theory to judge fairness.
  • Few trials give an unreliable estimate.

Worked examples

Example 1

A coin lands heads \(58\) times in \(100\) flips. Find the relative frequency.

Working

\[58 \div 100\]successes divided by trials
\[= 0.58\]state the relative frequency

Example 2

A spinner has probability \(0.25\) of red. How many reds are expected in \(120\) spins?

Working

\[0.25 \times 120\]multiply probability by trials
\[= 30\]state the expected number

Example 3

A dice gives a six \(45\) times in \(300\) rolls. Is it fair?

Working

\[45 \div 300 = 0.15\]find the relative frequency
\[\tfrac{1}{6} \approx 0.167\]compare with the theoretical probability
\[\text{Close, so probably fair}\]the difference is small over many trials

Common mistakes

  • Treating relative frequency as exact.

    It is an estimate, and it varies between experiments.

  • Judging fairness from few trials.

    A small number of trials gives an unreliable estimate.

  • Confusing expected with guaranteed.

    Expecting 30 reds does not mean exactly 30 will occur.

  • Dividing the wrong way round.

    It is successes over trials, not trials over successes.

Exam tips

  • State clearly that relative frequency is an estimate.
  • Use more trials for a more reliable estimate.
  • Multiply by the number of trials to find an expected value.
  • Compare with the theoretical probability when judging fairness.

Key terms

Relative frequency
An experimental estimate of probability.
Trial
One repetition of an experiment.
Expected value
Probability multiplied by the number of trials.
Bias
A tendency for one outcome to occur more often than it should.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.