Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Probability
Relative and Expected Frequencies
What is Relative and Expected Frequencies?
Relative frequency is the observed frequency of an outcome divided by the number of trials, and it is used as an experimental estimate of a probability when the theoretical probability is unknown or when a device may not be fair. It is an estimate rather than a guarantee: repeating the experiment can give a different value, and a longer run of trials usually gives a more stable estimate provided the conditions do not change. Expected frequency is the number of trials multiplied by the probability of the outcome, and the same relationship is used to estimate an expected value from a population by multiplying the population size by the probability. An expected frequency is a prediction made by the model rather than a promise about what must occur. A device is fair when its intended outcomes have the appropriate equal theoretical probabilities and biased when they do not, while an outcome is random when an individual result cannot be predicted with certainty in advance even though its probabilities may be known. Fairness is judged by comparing observed with expected frequencies while taking the number of trials into account, because a short surprising run is not by itself proof of bias.
This definition is part of the Probability chapter in Cambridge O Level Mathematics (Syllabus D).