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Statistics (from German: Statistik, orig. "description of a state, a country") [ 1][ 2] is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. [ 3][ 4][ 5] In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or ...
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [ note 1][ 1][ 2] A simple example is the tossing of a fair (unbiased) coin.
As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of data. [1] Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics or sequential estimation .
t. e. In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [ 1][ 2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events ( subsets of the sample space).
List of analyses of categorical data. List of fields of application of statistics. List of graphical methods. List of statistical software. Comparison of statistical packages. List of graphing software. Comparison of Gaussian process software. List of stochastic processes topics. List of matrices used in statistics.
Astrostatistics. Asymptotic distribution. Asymptotic equipartition property (information theory) Asymptotic normality – redirects to Asymptotic distribution. Asymptotic relative efficiency – redirects to Efficiency (statistics) Asymptotic theory (statistics) Atkinson index. Attack rate. Augmented Dickey–Fuller test.
With finite support. The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No ...
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.