Relative Frequency
What is relative frequency?
- Relative frequency is an estimate of a probability using results from an experiment
- For a certain number of trials of that experience, the probability of ‘success’ is:
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- If you flip an unfair coin 50 times and it lands on heads 20 times, an estimate for the probability of the coin landing on heads is (its relative frequency)
- That is the best estimate we can make, given the data we have
- We do not know the actual probability
- If you flip an unfair coin 50 times and it lands on heads 20 times, an estimate for the probability of the coin landing on heads is (its relative frequency)
- The more trials that are carried out, the more accurate relative frequency becomes
- It gets closer and closer to the actual probability
When will I be asked to use relative frequency?
- Relative frequency is used when actual probabilities are unavailable (or not possible to calculate)
- For example, if you do not know the actual probability of being left-handed, you can run an experiment to find an estimate (the relative frequency)
- Sometimes actual probabilities are known, as they can be calculated in theory (called theoretical probabilities)
- The theoretical probability of a fair coin landing on heads is 0.5
- The theoretical probability of a fair standard six-sided dice landing on a six is
- Relative frequency can be compared to a theoretical probability to test if a situation is fair or biased
- If 100 flips of the coin give a relative frequency of 0.48 for landing on heads, the coin is likely to be fair
- The theoretical probability is 0.5 and 0.48 is close to 0.5
- If 100 flips of the coin give a relative frequency of 0.13 for landing on heads, the coin is likely to be biased (not fair)
- If 100 flips of the coin give a relative frequency of 0.48 for landing on heads, the coin is likely to be fair
What else do I need to know about relative frequency?
- Relative frequency assumes that there is an equal chance of success on each trial
- The trials are independent of each other
- For example, if choosing something out of a bag (a ball, or marble etc), it would need to be replaced each time to use relative frequency
- The trials are independent of each other
Examiner Tip
- Exam questions will not necessarily use the phrase relative frequency.
- If you have to choose the best estimate, choose the one with the most trials.
Worked example
There are an unknown number of different coloured buttons in a bag.
Johan selects a button at random, notes its colour and replaces the button in the bag.
Repeating this 30 times, Johan notes that on 18 occasions he selected a red button.
Use Johan’s results to estimate the probability that a button drawn at random from the bag is red.
Taking ‘red’ to be a success, Johan had 18 successes out of a total of 30 trials.