Frequency (statistics)

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Histogram of travel time (to work), US 2000 census. Histograms depict the frequencies of observations occurring in certain ranges of values

In statistics the frequency (or absolute frequency) of an event i is the number n_i of times the event occurred in an experiment or study.[1]:12-19 These frequencies are often graphically represented in histograms.

Cumulative frequency refers to 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 refers to the absolute frequency normalized by the total number of events:

 f_i = \frac{n_i}{N} = \frac{n_i}{\sum_j n_j}.

The values of f_i for all events i can be plotted to produce a frequency distribution.

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.

See also[edit]


  1. ^ a b Kenney, J. F.; Keeping, E. S. (1962). Mathematics of Statistics, Part 1 (3rd ed.). Princeton, NJ: Van Nostrand Reinhold.