In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 the frequency of an event

Event (probability theory)

In probability theory, an event is a set of outcomes to which a probability is assigned. Typically, when the sample space is finite, any subset of the sample space is an event...

 i is the number n_i of times the event occurred in the experiment

Experiment

An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

 or the study. These frequencies are often graphically represented in histogram

Histogram

In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson...

s.

We speak of absolute frequencies, when the counts

Counting

Counting is the action of finding the number of elements of a finite set of objects. The traditional way of counting consists of continually increasing a counter by a unit for every element of the set, in some order, while marking those elements to avoid visiting the same element more than once,...

 n_i themselves are given and of (relative) frequencies, when those are normalized

Normalizing constant

The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics.-Definition and examples:In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e.g.,...

 by the total number of events:

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

Frequency distribution

In statistics, a frequency distribution 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...

.

The relative frequency density of the occurrence of an event is the score divided by the total number of observations.

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:

Relative frequency / (Upper extreme of class − lower extreme of class) = density

0.0625 / (30 − 15) = 0.0625 / 15 = 0.0041666.. That is: 0.00417 to 5 decimal places.

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

Frequency probability

Frequency probability is the interpretation of probability that defines an event's probability as the limit of its relative frequency in a large number of trials. The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the...

 of probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

. 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

Bayesian probability

Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is...

.

See also

• Probability density function
  Probability density function
  In probability theory, a probability density function , or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the...
  
  
• Frequency
  Frequency
  Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
  
  
• Law of large numbers
  Law of large numbers
  In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times...
  
  
• Statistical regularity
  Statistical regularity
  Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity...