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A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers. [1] There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics.
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 ...
Mean of a function. Formula for the average value of a function over its domain. In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f ( x) over the interval ( a, b) is defined by: [1] {\displaystyle {\bar {f ...
In mathematics and statistics, a circular mean or angular mean is a mean designed for angles and similar cyclic quantities, such as times of day, and fractional parts of real numbers . This is necessary since most of the usual means may not be appropriate on angle-like quantities. For example, the arithmetic mean of 0° and 360° is 180 ...
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of the possible values a random variable can take, weighted by the ...
In ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list. For example, the mean average of the numbers 2, 3, 4, 7, and 9 (summing to ...
Assumed mean. In statistics the assumed mean is a method for calculating the arithmetic mean and standard deviation of a data set. It simplifies calculating accurate values by hand. Its interest today is chiefly historical but it can be used to quickly estimate these statistics. There are other rapid calculation methods which are more suited ...
Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...