Frequency (statistics)

The cumulative frequency is the total of the absolute frequencies of all events at or below a certain point in an ordered list of events.[1]^:17–19

The relative frequency (or empirical probability) of an event is the absolute frequency normalized by the total number of events:

${\displaystyle f_{i}={\frac {n_{i}}{N}}={\frac {n_{i}}{\sum _{j}n_{j}}}.}$

The values of ${\displaystyle f_{i}}$ for all events ${\displaystyle i}$ can be plotted to produce a frequency distribution.

In the case when ${\displaystyle n_{i}=0}$ for certain i, pseudocounts can be added.

The following are some commonly used methods of depicting frequency:[2]

Bar graphs

Example of a bar chart, with 'Country' as the categorical variable for the discrete data set.

Example of a horizontal 3D bar chart

A bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column bar chart.

Under the frequency interpretation of probability, it is assumed that as the length of a series of trials increases without bound, the fraction of experiments in which a given event occurs will approach a fixed value, known as the limiting relative frequency.[5][6]

This interpretation is often contrasted with Bayesian probability. In fact, the term 'frequentist' was first used by M. G. Kendall in 1949, to contrast with Bayesians, whom he called "non-frequentists".[7][8] He observed

3....we may broadly distinguish two main attitudes. One takes probability as 'a degree of rational belief', or some similar idea...the second defines probability in terms of frequencies of occurrence of events, or by relative proportions in 'populations' or 'collectives'; (p. 101)

...

12. It might be thought that the differences between the frequentists and the non-frequentists (if I may call them such) are largely due to the differences of the domains which they purport to cover. (p. 104)

...

I assert that this is not so ... The essential distinction between the frequentists and the non-frequentists is, I think, that the former, in an effort to avoid anything savouring of matters of opinion, seek to define probability in terms of the objective properties of a population, real or hypothetical, whereas the latter do not. [emphasis in original]

• Aperiodic frequency
• Cumulative frequency analysis
• Law of large numbers
• Multiset multiplicity as frequency analog
• Probability density function
• Statistical regularity
• Word frequency