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Jump to navigation N power company values to search This article is about the mathematical concept. For the state of being mean or cruel, see meanness.

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For a broader coverage of this topic, see average. There are several kinds of mean in various branches of mathematics. For a data set, the arithmetic mean, also called the mathematical expectation or average, is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. An analogous formula applies to the case of a continuous probability distribution. Moreover, for some distributions the mean is infinite. For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population.

For example, the population mean height is equal to the sum of the heights of every individual divided by the total number of individuals. The sample mean may differ from the population mean, especially for small samples. Equality holds if and only if all the elements of the given sample are equal. Geometric visualization of the mode, median and mean of an arbitrary probability density function. The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. In this context, it is also known as the expected value. In all cases, including those in which the distribution is neither discrete nor continuous, the mean is the Lebesgue integral of the random variable with respect to its probability measure.