distribution (statistical or frequency)

distribution (statistical or frequency) A series of figures presenting all observed values (as raw numbers or proportion of cases) for a variable in a quantitative data-set—enabling a quick visual appreciation of the distribution of the data. The frequency distribution may be further illustrated by use of graphics such as a pie-chart or histogram.

A frequency or statistical distribution using observed data should not be confused with mathematical probability distributions, which are hypothetical distributions, the form of which is determined by algebraic formulae. The correspondence between an observed frequency distribution and various hypothetical mathematical distributions will often determine the type of statistical analysis performed on particular data.

Frequency distributions from a survey data-set are usually the first output from the clean and edited data-set, showing the response totals for each possible reply to each question in the questionnaire. Empirically observed distributions can be analysed using measures of dispersion and other statistical tools developed from the three main forms of probability distribution: binomial, Poisson, and normal (Gaussian).