# Frequency (statistics)

In statistics the frequency of an event i is the number ni of times the event occurred in the experiment or the study. These frequencies are often graphically represented in histograms.

We speak of absolute frequencies, when the counts ni themselves are given and of (relative) frequencies, when those are normalized by the total number of events:

$f_i = \frac{n_i}{N} = \frac{n_i}{\sum_i n_i}$

Taking the fi for all i and tabulating or plotting them leads to a frequency distribution.

The relative frequency density of occurrence of an event is the relative frequency of i divided by the size of the bin used to classify i.

For example: If the lower extreme of the class you are measuring the density of is 15 and the upper extreme of the class you are measuring is 30, given a relative frequency of 0.0625, you would calculate the frequency density for this class to be:

Rel.freq / (Upper Extreme of Class - Lower Extreme of Class) = Density

0.0625 / (30 - 15) = 0.0625 / 15 = 0.0041666.. That is: 0.00417 to 5 S.F.

In biology, relative frequency is the occurrence of a single gene in a specific species that makes up a gene pool.

The limiting relative frequency of an event over a long series of trials is the conceptual foundation of the frequency interpretation of probability. In this framework, it is assumed that as the length of the series increases without bound, the fraction of the experiments in which we observe the event will stabilize. This interpretation is often contrasted with Bayesian probability.