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Expected Frequency

FoundationHigherAQAEdexcel

Practise Expected Frequency for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Expected frequency is the probability of an event multiplied by the number of trials.

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

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Expected frequency is the number of times an event is expected to occur in a given number of trials.

The formula is \(\text{expected frequency} = \text{probability} \times \text{number of trials}\).

The word expected is doing careful work here. It gives the most likely number, not a guarantee — rolling a fair dice 60 times gives an expected 10 sixes, but getting exactly 10 would be somewhat lucky. The actual number will usually be close to the expected value, and closer proportionally as the number of trials increases.

Revision notes

The formula

Expected frequency \(=\) probability \(\times\) number of trials.

Multiply the probability of the event by how many trials are carried out. The answer is usually rounded to a whole number, since events occur a whole number of times.

What expected means

It gives the most likely number of occurrences, not a guaranteed one.

Rolling a fair dice 60 times gives an expected 10 sixes, but the actual number will vary. Saying the result 'will be' 10 rather than 'is expected to be' 10 loses marks.

Working backwards

Probability \(= \frac{\text{expected frequency}}{\text{number of trials}}\).

This is used when the expected frequency is given and the probability must be found, or to check an answer by reversing the calculation.

Key points

  • Expected frequency = probability × trials.
  • It gives the most likely number.
  • It is not a guarantee.
  • The actual number will vary.
  • Round to a whole number where appropriate.
  • Probability = expected frequency ÷ trials.

Worked examples

Example 1

A dice is rolled 90 times. Work out the expected number of fours. [2 marks]

Working

\(P(\text{four}) = \frac{1}{6}\), so expected frequency \(= \frac{1}{6} \times 90\)multiply the probability by the number of trials
\(= 15\)work out the expected frequency

Example 2

A spinner has probability 0.25 of landing on red. It is spun 120 times. Work out the expected number of reds. [2 marks]

Working

Expected frequency \(= 0.25 \times 120\)multiply the probability by the number of trials
\(= 30\)work out the expected frequency

Example 3

Explain why the actual frequency may differ from the expected frequency. [2 marks]

Working

Expected frequency gives the most likely number rather than a guaranteed onestate what it means
so chance variation means the actual number of occurrences will usually differ slightlyexplain why they differ

Common mistakes

  • Saying the expected frequency will definitely occur.

    It is the most likely value, not a certainty.

  • Dividing instead of multiplying.

    Expected frequency is probability × trials.

  • Leaving a decimal answer for a count.

    Round to a whole number where the context requires it.

  • Using the wrong probability.

    Check the probability applies to the event being counted.

Exam tips

  • Multiply probability by the number of trials.
  • Use the word 'expected' in your answer.
  • Round sensibly for counts of events.
  • Reverse the formula to find a probability.

Key terms

Expected frequency
The most likely number of occurrences in a set of trials.
Trial
One repetition of an experiment.
Chance variation
Random difference between expected and actual results.
Probability
The likelihood of an event occurring.

Related topics

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