Probability vs Relative Frequency
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Probability
Probability
Probability is a number from 0 to 1 measuring how likely an event is, with 0 meaning impossible and 1 meaning certain.
Probability measures the long-run relative frequency of an event over many repetitions. For equally likely outcomes, . For example, rolling an even number on a fair six-sided die has probability . Over many rolls the fraction of even results settles near this value, an idea called the law of large numbers.
Relative frequency
Describing data
A relative frequency is the count in a category divided by the total number of observations, giving a proportion of the whole.
Relative frequency rescales a raw count into a fraction or percent, which makes groups of different sizes comparable. For example, if 18 of 40 students walk to school, the relative frequency is , or 45 percent. The relative frequencies across all categories add up to , that is, 100 percent. This idea is the empirical basis for estimating probabilities from data.