Relative frequency
Objective. Use experimental results to estimate future outcomes.
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- 2. Worked example
- 3. Practice
- 4. Feedback
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Learn: the key idea
Relative frequency is an estimate of probability found by dividing the number of times an event occurs by the total number of trials in an experiment. As the number of trials increases, relative frequency tends to settle closer to the true theoretical probability, making larger samples more reliable. Example: if a drawing pin lands point-up 68 times out of 100 throws, the relative frequency is 68 ÷ 100 = 0.68, used to estimate the probability of landing point-up. This estimate can then predict future outcomes, such as expecting about 0.68 × 50 = 34 point-up landings in 50 more throws.
Worked example
A biased die is rolled 80 times and lands on a six 20 times. Find the relative frequency of rolling a six.
- 1Relative frequency is found by dividing successes by total trials.
- 2Identify the successes (20) and total trials (80).
- 3Divide: 20 ÷ 80.
- 4The relative frequency of rolling a six is 0.25.
Answer: 0.25
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Start practisingCommon mistake. Pupils sometimes treat a small number of trials as giving a perfectly reliable probability; always note that more trials generally give a more trustworthy estimate of relative frequency.
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