In statistics the frequency of an event is the number of times the event occurred in an experiment or study. These frequencies are often graphically represented in histograms.
Types
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. The of an event is the absolute frequency normalized by the total number of events: The values of for all events can be plotted to produce a frequency distribution. In the case when for certain i, pseudocounts can be added.
Depictions
The following are some commonly used methods of depicting frequency:
Histograms
A histogram is a representation of tabulated frequencies, shown as adjacent rectangles or squares, erected over discrete intervals, with an area proportional to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data. A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the total area equaling 1. The categories are usually specified as consecutive, non-overlapping intervals of a variable. The categories must be adjacent, and often are chosen to be of the same size. The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous.
A frequency distribution table is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample. An example is shown below
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. 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". He observed
