Variance - History

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 ...

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• 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

In general, the population variance of a finite population is given by where is the population mean. This is merely a special case of the general definition of variance introduced above, but restricted to finite populations. In many practical situations, the true variance of a population is not known a priori and must be computed somehow. When dealing with large finite populations, it is almost never possible to find the exact value of the population variance, due to time, cost, and other resource constraints. W ...

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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

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

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