Mean Statistic Value

A Mean Statistic Value is a point estimate that is calculated by a mean function (which describes the central tendency of a numeric set).

• Context:
  • It can range from being a Population Mean Value to being a Sample Mean Value.
  • It can range from being an Arithmetic Mean Value to being a Geometric Mean Value to being a Harmonic Mean Value.
• Example(s):
  • 5 is the arithmetic mean of the population {1,5,9), .
  • 3 is the sample mean of the sample {1,5), .
  • …
• Counter-Example(s):
  • a Median Value.
  • a Maximum Value.
• See: Mode Value, Discrete Probability Distribution, Statistical Population, Expected Value, Central Tendency.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/mean Retrieved:2015-6-28.
  • In mathematics, mean has several different definitions depending on the context.

    In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together, giving [math]\displaystyle{ \mu = \sum x P(x) }[/math] . An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean; see the Cauchy distribution for an example. Moreover, for some distributions the mean is infinite: for example, when the probability of the value [math]\displaystyle{ 2^n }[/math] is [math]\displaystyle{ \tfrac{1}{2^n} }[/math] for n = 1, 2, 3, .... For a data set, the terms arithmetic mean, mathematical expectation, and sometimes average are used synonymously to refer to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x₁, x₂, ..., x_n is typically denoted by [math]\displaystyle{ \bar{x} }[/math] , pronounced "x bar". If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is termed the sample mean (denoted [math]\displaystyle{ \bar{x} }[/math] ) to distinguish it from the population mean (denoted [math]\displaystyle{ \mu }[/math] or [math]\displaystyle{ \mu_x }[/math]). 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. The law of large numbers dictates that the larger the size of the sample, the more likely it is that the sample mean will be close to the population mean.

    Outside of probability and statistics, a wide range of other notions of "mean" are often used in geometry and analysis; examples are given below.

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