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, P(A)=number of outcomes in Atotal number of outcomesP(A) = \frac{\text{number of outcomes in } A}{\text{total number of outcomes}}. For example, rolling an even number on a fair six-sided die has probability 3/6=0.53/6 = 0.5. Over many rolls the fraction of even results settles near this value, an idea called the law of large numbers.

Full entry for probability

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 18/40=0.4518 / 40 = 0.45, or 45 percent. The relative frequencies across all categories add up to 11, that is, 100 percent. This idea is the empirical basis for estimating probabilities from data.

Full entry for relative frequency

Where each one fits in the course