In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. The variance of a real-valued random variable is its second central moment, and it also happens to be its second cumulant. The variance of a random variable is the square of its standard deviation. Variance - Definition. If μ = E(X) is the expected value (mean) of the random variable X, then the variance is ...

Including:

Variance - Definition Variance - Properties Variance - Population variance and sample variance
Variance - An unbiased estimator
Variance - Generalizations Variance - History Variance - Moment of inertia

Read more here: » Variance: Encyclopedia - Variance

See also:

Variance, Variance - Definition, Variance - Properties, Variance - Population variance and sample variance, Variance - An unbiased estimator, Variance - Generalizations, Variance - History, Variance - Moment of inertia

Read more here: » Variance: Encyclopedia II - Variance - Population variance and sample variance

If the variance is defined, we can conclude that it is never negative because the squares are positive or zero. The unit of variance is the square of the unit of observation. For example, the variance of a set of heights measured in centimeters will be given in square centimeters. This fact is inconvenient and has motivated many statisticians to instead use the square root of the variance, known as the standard ...

See also:

Variance, Variance - Definition, Variance - Properties, Variance - Population variance and sample variance, Variance - An unbiased estimator, Variance - Generalizations, Variance - History, Variance - Moment of inertia

Read more here: » Variance: Encyclopedia II - Variance - Properties

The Allan variance, named after David W. Allan, is a measurement of accuracy in clocks. It is also known as the two-sample variance. It is defined as one half of the time average of the squares of the differences between successive readings of the frequency deviation sampled over the sampling period. For most real-world systems, the Allan variance depends on the time period used between samples: therefore it is a function of the sample period, as well as the distribution being measured. A low Allan variance is a characteristic of a clock with good stability over the measured period. < ...

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A Jewish holiday or Jewish Festival is a day or series of days observed by Jews as holy or secular commemorations of important events in Jewish history. In Hebrew, Jewish holidays and festivals, depending on their nature, may be called Yom Tov ("good day") or chag ("festival") or ta'nit ("fast"). Outside of a Jewish context, all Jewish holidays appear to be "religious holidays" but that is not actually the case. It is important to understand that Judaism is so old that it is simultaneously a religion ...

Including:

Jewish holiday - Rosh Hashanah - The Jewish New Year Jewish holiday - Aseret Yemei Teshuva - Ten Days of Repentance Jewish holiday - Yom Kippur - Day of Atonement Jewish holiday - Sukkot - Festival of Booths Jewish holiday - Shemini Atzeret and Simchat Torah - Rejoicing with the Law Jewish holiday - Hanukkah - Festival of Lights Jewish holiday - Tu Bishvat - New year of the trees Jewish holiday - Purim - Festival of Lots Jewish holiday - New Year for Kings Jewish holiday - Pesach - Passover Jewish holiday - Sefirah - Counting of the Omer
Jewish holiday - Lag Ba'omer
Jewish holiday - New Israeli/Jewish national holidays
Jewish holiday - Yom Ha'Shoah - Holocaust Remembrance day Jewish holiday - Yom Hazikaron - Memorial Day Jewish holiday - Yom Ha'atzma'ut - Israel Independence Day Jewish holiday - Yom Yerushalayim - Jerusalem Day
Jewish holiday - Shavuot - Pentecost Jewish holiday - The Three Weeks and the Nine Days Jewish holiday - Tisha B'av - Ninth of Av Jewish holiday - Tithe of animals Jewish holiday - Rosh Chodesh - the New Month Jewish holiday - Shabbat - The Sabbath יום השבת Jewish holiday - Variances in observances

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Stratification is the building up of layers of deposits, and can have several variations of meaning: Social stratification, is the dividing of a society into levels based on wealth or power. Stratification in archaeology are the layers in which objects are found. Stratification (botany). See stratified sampling for the use of stratification in survey sampling. The term "stratified sampling" is also refers a method of variance reduction in Monte Carlo methods. In logic, stratifica

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Agnostic atheism is the philosophy that encompasses both atheism and agnosticism. Due to definitional variance, an agnostic atheist does not believe in God or gods and by extension holds true one or more of these statements: The existence and nonexistence of deities is currently unknown and maybe absolutely unknowable. Knowledge of the existence and nonexistence of deities is irrelevant or unimportant. Abstention from claims of knowledge of the e ...

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Heterodoxy includes "any opinions or doctrines at variance with an official or orthodox position". [1] As an adjective, heterodox is used to describe a subject as "characterized by departure from accepted beliefs or standards" (status quo). The noun heterodoxy is synonymous with unorthodoxy and heresy, while the adjective heterodox is synonymous with dissident and heretical. Including:

Heterodoxy - Definition Heterodoxy - Ecclesiastic usage
Heterodoxy - Eastern Orthodoxy Heterodoxy - Roman Catholicism Heterodoxy - Other denominations
Heterodoxy - Footnotes
Heterodoxy - Other articles Heterodoxy - External links

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If X is a vector-valued random variable, with values in Rn, and thought of as a column vector, then the natural generalization of variance is E[(X − μ)(X − μ)T], where μ = E(X) and XT is the transpose of X, and so is a row vector. This variance is a nonnegative-definite square matrix, commonly referred to as the covariance matrix. If X is a complex-valued random variable, then its variance is E[(X − μ)(X − μ)*], where X* is the complex conjugate of X. ...

See also:

Variance, Variance - Definition, Variance - Properties, Variance - Population variance and sample variance, Variance - An unbiased estimator, Variance - Generalizations, Variance - History, Variance - Moment of inertia

Read more here: » Variance: Encyclopedia II - Variance - Generalizations

In general, zoning is the division of an area into sub-areas, called zones. This article primarily concerns zoning in its urban planning iteration. Zoning - Land use. Zoning is a system of land use regulation which designates the permitted uses of land based on mapped zones, which separate one part of the community from another. Zoning regulations fall under the police power rights governments may exercise over real property. Theoretically, its primary purpose is to segregate uses that are thought to ...

Including:

Zoning - Land use Zoning - Origins and History of Zoning Zoning - Constitutional Challenges Zoning - Some limitations and criticisms of zoning
Zoning - Circumventions Zoning - Social criticisms Zoning - Exclusionary zoning and housing affordability
Zoning - Other uses of the concept of zoning
Zoning - Pricing Zoning - Environmental controls Zoning - Permaculture / agricultural design Zoning - Informational

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If μ = E(X) is the expected value (mean) of the random variable X, then the variance is That is, it is the expected value of the square of the deviation of X from its own mean. In plain language, it can be expressed as "The average of the square of the distance of each data point from the mean". It is thus the mean squared deviation. The variance of random variable X is typically designated as , , or simply σ2. Note that the above definition can be used for both di ...

See also:

Variance, Variance - Definition, Variance - Properties, Variance - Population variance and sample variance, Variance - An unbiased estimator, Variance - Generalizations, Variance - History, Variance - Moment of inertia

Read more here: » Variance: Encyclopedia II - Variance - Definition

Binarization of the vector x into its adjacent implicational matrix, shown below and subtraction of the transpose of this binarized implicational matrix from itself (cf., matrix subtraction) results in the same skew symmetric matrix as that of the major difference of the vector x. This matrix can be triangularized, into a skew asymmetrix matrix. The above matrix can provide information about the number of bits contained by the data, ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

Read more here: » True variance: Encyclopedia II - True variance - Variance and Information

The variance can be easily changed from the true variance to the unbiased variance, as and from the unbiased variance to the true variance, as For the example, the true variance (1.25) can be changed to the unbiased variance as (4/3)(1.25) = 1.67 and the unbiased variance (1.67) can be changed to the true variance as (3/4)(1.67) = 1.25. ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

Read more here: » True variance: Encyclopedia II - True variance - Changing true variance to unbiased variance and vice versa

Mathematical formulae defining the true and the unbiased variance use the Greek letter Σ which means sum all values of a variable. The variable in this context is the lowercase Latin character x which denotes the deviation scores. The number of values of the variable X is signified as n. The values of the variable X are the obtained values , sometimes also called the obtained scores, i.e., values of the variable X obtained from quantification of properties of some entity or some ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

Read more here: » True variance: Encyclopedia II - True variance - Computation of the true and unbiased variance

Using matrix algebra, the true variance can be measured by computing all possible differences between elements of a population. Consider that a major difference of a vector results in a skew-symmetric matrix with elements describing all possible differences between its values. For instance, the major difference of the vector x [0, 1, 2, 3] with true variance equal to 1.25 and unbiased variance equal to 1.67, The above matrix contains the information necessary to compute either the true variance, or the unbised variance. ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

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There are three conceptual classes of such models: Fixed-effects model assumes that the data come from normal populations which differ in their means. Random-effects models assume that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy. Mixed models describe situations where both fixed and random effects are present. The fundamental technique is a partitioning of the total sum of squares into components related to the effects in the model used ...

See also:

Analysis of variance, Analysis of variance - Overview, Analysis of variance - Fixed-effects model, Analysis of variance - Random-effects model, Analysis of variance - Degrees of freedom, Analysis of variance - Tests of significance

Read more here: » Analysis of variance: Encyclopedia II - Analysis of variance - Overview

In statistics, the term true variance is often used to refer to the unobservable variance of a whole population, as distinguished from an observable statistic based on a sample. Suppose a number, such as a person's height or income or age or cholesterol level, is assigned to every member of a population of n individuals. Let xi be the number assigned to the ith individual, for i = 1, ..., n. Then ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

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The n-1 term in the denominator of the unbiased variance formula is referred to as degrees of freedom, signified as df or by the Greek letter ν. The notion of the degrees of freedom is related to the concept of the random normal variable. To illustrate this concept, let us consider the numbers 0, 1, 2, 3 assigned to five subjects in our illustrative example. These subjects are fictitious, as are the numbers 0, 1, 2, and 3. Don't be misled by their ordinality, as in a recent lot ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

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The above definition of variance in terms of differences contained by the data does not involve the arithmetic mean. It seems plausible to assume that the information contained in the above matrix could have been also obtained from a matrix of all possible differences between the data elements and their mean, which can be obtained as Squaring the elements of the above matrix results in a matrix with n columns of squared deviation scores x with column sums (5.00) divided by n (4) equal to the variance computed by divid ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

Read more here: » True variance: Encyclopedia II - True variance - Differences between data elements and their mean

Using all possible differences between values of a variable as a foundation of statistical theory was contemplated by Kendall (1943, p. 47) who defined a coefficient, called here u², as For the discontinuous infinite case, the above equation can be written as and for the finite case as where the summed term in the above equation is a vector of all possible differences between elements of v ...

See also:

True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

Read more here: » True variance: Encyclopedia II - True variance - True variance and all possible differences between values of a variable