Knowledge Organiser: Expected Frequency
This topic summary covers Knowledge Organiser: Expected Frequency within Expected Frequency for GCSE Mathematics. Revise Expected Frequency in Probability for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
14 questions
Recall
12 flashcards
Knowledge Organiser: Expected Frequency
Key Terms
- Expected frequency: The predicted number of times an event occurs in n trials
- Theoretical probability: Probability calculated from equally likely outcomes
- Experimental probability: Probability estimated from the results of actual trials
- Trial: A single attempt or observation in an experiment
- Relative frequency: Experimental probability = number of successes ÷ number of trials
Must-Know Facts
- Expected frequency = probability × number of trials
- Expected frequency is a prediction — actual results will vary
- The more trials performed, the closer actual results get to expected results
- Expected frequency can be a decimal — round sensibly for real-world contexts
- Either theoretical or experimental probability can be used in the formula
- Used in quality control, risk assessment, and planning
Key Formulas
- Expected frequency = probability × number of trials
- Experimental probability = number of successful outcomes ÷ total trials
- Expected frequency = (experimental probability) × (number of future trials)
Common Mistakes
- Expected ≠ actual: Expected frequency is a prediction — the actual result may differ, especially with few trials
- Using relative frequency as theoretical probability: Experimental probability approaches theoretical only as the number of trials increases
- Wrong formula direction: Expected frequency = P × n (probability × trials), not P ÷ n
- Biased vs fair: If experimental probability differs significantly from theoretical, the experiment may be biased
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Practice Questions for Expected Frequency
Which formula correctly gives the expected frequency of an event?
A fair coin is flipped 50 times. The expected number of heads is 25. In the actual experiment, only 18 heads are recorded. Explain why the actual number of heads may differ from the expected number of heads.
Quick Recall Flashcards
14 questions on Expected Frequency — practise free
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