In statistics, a frequency distribution is a list of the values that a variable takes in a sample. It is usually a list, ordered by quantity, showing the number of times each value appears. For example, if 100 people rate a five-point Likert scale assessing their agreement with a statement on a scale on which 1 denotes strong agreement and 5 strong disagreement, the frequency distribution of their responses might look like: A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... In mathematics, a probability distribution assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. ... A Likert scale (pronounced lick-ert) is a type of psychometric scale often used in questionnaires. ...

This simple tabulation has two drawbacks. When a variable can take continuous values instead of discrete values or when the number of possible values is too large, the table construction is cumbersome, if it is not impossible. A slightly different tabulation scheme based on the range of values is used in such cases. For example, if we consider the heights of the students in a class, the frequency table might look like below. This article needs to be cleaned up to conform to a higher standard of quality. ...

Applications

Operating and managing on frequency tabulated data is much simpler than operation on raw data. There are simple algorithms to calculate median, mean, standard deviation etc. from these tables.

Statistical hypothesis testing is founded on the assessment of differences and similarities between frequency distributions. This assessment involves measures of central tendency or averages, such as the mean and median, and measures of variability or statistical dispersion, such as the standard deviation or variance. One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. ... In mathematics, an average or central tendency of a set (list) of data refers to a measure of the middle of the data set. ... In mathematics, there are numerous methods for calculating the average or central tendency of a list of n numbers. ... In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ... In probability theory and statistics, a median is a number dividing the higher half of a sample, a population, or a probability distribution from the lower half. ... In descriptive statistics, statistical dispersion (also called statistical variability) is quantifiable variation of measurements of differing members of a population within the scale on which they are measured. ... In probability and statistics, the standard deviation is a measure of the mean distance of values in a data set from their mean. ... In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ...

A frequency distribution is said to be skewed when its mean and median are different. The kurtosis of a frequency distribution is the concentration of scores at the mean, or how peaked the distribution appears if depicted graphically—for example, in a histogram. If the distribution is more peaked than the normal distribution it is said to be leptokurtic; if less peaked it is said to be platykurtic. In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. ... In probability theory and statistics, kurtosis is a measure of the peakedness of the probability distribution of a real-valued random variable. ... In statistics, a histogram is a graphical display of tabulated frequencies. ... The normal distribution, also called Gaussian distribution (although Gauss was not the first to work with it), is an extremely important probability distribution in many fields. ...

Frequency distributions are also used in frequency analysis to crack codes and refer to the relative frequency of letters in different languages. In mathematics, physics and signal processing, frequency analysis is a method to decompose a function, wave, or signal into its frequency components so that it is possible to have the frequency spectrum. ...