Sheet № 188 · Foundation + Higher · AQA · Edexcel · OCR
Relative Frequency –
Relative frequency is a key probability concept tested on both Foundation and Higher GCSE Maths papers across AQA, Edexcel and OCR. When you cannot calculate a theoretical probability — for example because a dice might be biased or a spinner's sections are not equal — you use experimental results instead. Relative frequency provides an es
§Key definitions
Relative frequency
(also called experimental probability) estimates the probability of an event based on the results of an experiment or collected data.
Question:
A drawing pin is dropped 50 times. It lands point-up 18 times. Estimate the probability that it lands point-up.
Answer:
The estimated probability of landing point-up is 0.36.
(a)
After 50: 12/50 = 0.24. After 100: 21/100 = 0.21. After 200: 38/200 = 0.19. After 500: 84/500 = 0.168.
(b)
The estimate after 500 trials is the most reliable because relative frequency becomes more accurate as the number of trials increases.
§Formulas to memorise
Relative frequency = Number of times the event occurs ÷ Total number of trials
Relative frequency: (also called experimental probability) estimates the probability of an event based on the results of an experiment or collected data.
Divide: relative frequency = event occurrences ÷ total trials.
Relative frequency = 18 ÷ 50 = 0.36.
Relative frequency of heads = 212 ÷ 400 = 0.53.
Worked example
A drawing pin is dropped 50 times. It lands point-up 18 times. Estimate the probability that it lands point-up.
Working:
⚠ Common mistakes
- ✗Calling relative frequency exact. It is always an estimate — use this word in your answer.
- ✗Using too few trials to draw conclusions. A small number of trials produces unreliable estimates. Always mention that more trials would improve accuracy.
- ✗Confusing relative frequency with theoretical probability. Relative frequency is based on experimental results; theoretical probability is calculated from equally likely outcomes.
✦ Exam tips
- →Always use the word "estimate" when referring to relative frequency — this shows the examiner you understand the concept.
- →If a table shows relative frequencies for increasing numbers of trials, the most reliable estimate is always the one with the most trials.
- →To predict future outcomes, multiply the relative frequency by the number of future trials.
- →Questions often combine relative frequency with expected frequency — see expected frequency.
- →For foundational probability, see probability scale and basic probability. For key formulas, visit our GCSE Maths formulas page.