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Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. [1][2]
Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, [8] or as a branch of mathematics. [9] Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data ...
The generalized mean, also known as the power mean or Hölder mean, is an abstraction of the quadratic, arithmetic, geometric, and harmonic means. It is defined for a set of n positive numbers xi by. [1] By choosing different values for the parameter m, the following types of means are obtained: maximum of. quadratic mean.
Statistic. A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic.
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. [1] When referring specifically to probabilities, the corresponding ...
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
In mathematics and statistics, the arithmetic mean ( / ˌærɪθˈmɛtɪk ˈmiːn / arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. [1] The collection is often a set of results from an experiment, an ...
Deviation (statistics) In mathematics and statistics, deviation serves as a measure to quantify the disparity between an observed value of a variable and another designated value, frequently the mean of that variable. Deviations with respect to the sample mean and the population mean (or "true value") are called errors and residuals, respectively.