“variance”的概念、定义、翻译、参考文献-科学参考

variance

Physics

A continuous distribution that has a probability density function f(x) has a variance σ‎² defined by

$σ^{2} = \int_{- \infty}^{\infty} {(x - μ)}^{2} f (x) d x,$

where μ‎ is defined by

$μ = \int_{- \infty}^{∞} x f (x) d x .$

If the distribution is discrete, with a probability function p(x), the variance σ‎² is defined by σ‎²=∑‎(x − μ‎)²px, where μ‎ is defined by $μ = \sum_{x} x p (x) .$

Mathematics

A measure of the dispersion of a random variable or of a sample. For a random variable X, the population variance is the second moment about the population mean μ‎ and is equal to E((X − μ‎)²) (see expected value). It is usually denoted by σ‎² or Var(X). For a sample, the sample variance, denoted by s², is the second moment of the data about the sample mean $\bar{x}$ , but the denominator is usually taken as n − 1 rather than n in order to make it an unbiased estimator of the population variance. So

$s^{2} = \frac{\sum {(x_{i} - \bar{x})}^{2}}{n - 1} .$

For computational purposes, notice that $\sum {(x_{i} - \bar{x})}^{2} = \sum x_{i}^{2} - n {\bar{x}}^{2}$ .

Statistics

The word ‘variance’ is used as a shorthand for either the population variance or the sample variance, depending on context. It is the square of the standard deviation.

Chemical Engineering

A statistical measure of the dispersion of a set of data from the mean. The variance is equal to the square of the standard deviation and is used to distinguish between probability distributions.

Computer

See measures of variation.

Geology and Earth Sciences

In statistics, a measure of the spread of the data about the mean. In a set of data, the square of the mean variation about the mean value. It is calculated as the mean of the squared data points minus the mean squared; the standard deviation of a data set is the square root of the variance: $s^{2} = ({\sum_{i = 1}^{i = n} (x_{i} - \bar{x})}^{2}) / n$ where s² is the variance, x_i is the mean value of the ith measurement of x, x̄‎ is the mean value of x, and n is the number of measurements.

Economics

A measure of dispersion of probability distribution. The population variance of a random variable X is Var(X) = E[(X − E[X])²], where E denotes expected value. The sample variance of a set of N observations {x_i}, i = 1, 2,…, N, is given by

$V = \frac{1}{N} \sum_{i = 1}^{N} {(x_{i} - μ)}^{2},$

where μ‎ is the sample mean. See also covariance matrix.

单词	variance
释义	variance Physics A continuous distribution that has a probability density function f(x) has a variance σ‎² defined by $σ^{2} = \int_{- \infty}^{\infty} {(x - μ)}^{2} f (x) d x,$ where μ‎ is defined by $μ = \int_{- \infty}^{∞} x f (x) d x .$ If the distribution is discrete, with a probability function p(x), the variance σ‎² is defined by σ‎²=∑‎(x − μ‎)²px, where μ‎ is defined by $μ = \sum_{x} x p (x) .$ Mathematics A measure of the dispersion of a random variable or of a sample. For a random variable X, the population variance is the second moment about the population mean μ‎ and is equal to E((X − μ‎)²) (see expected value). It is usually denoted by σ‎² or Var(X). For a sample, the sample variance, denoted by s², is the second moment of the data about the sample mean $\bar{x}$ , but the denominator is usually taken as n − 1 rather than n in order to make it an unbiased estimator of the population variance. So $s^{2} = \frac{\sum {(x_{i} - \bar{x})}^{2}}{n - 1} .$ For computational purposes, notice that $\sum {(x_{i} - \bar{x})}^{2} = \sum x_{i}^{2} - n {\bar{x}}^{2}$ . Statistics The word ‘variance’ is used as a shorthand for either the population variance or the sample variance, depending on context. It is the square of the standard deviation. Chemical Engineering A statistical measure of the dispersion of a set of data from the mean. The variance is equal to the square of the standard deviation and is used to distinguish between probability distributions. Computer See measures of variation. Geology and Earth Sciences In statistics, a measure of the spread of the data about the mean. In a set of data, the square of the mean variation about the mean value. It is calculated as the mean of the squared data points minus the mean squared; the standard deviation of a data set is the square root of the variance: $s^{2} = ({\sum_{i = 1}^{i = n} (x_{i} - \bar{x})}^{2}) / n$ where s² is the variance, x_i is the mean value of the ith measurement of x, x̄‎ is the mean value of x, and n is the number of measurements. Economics A measure of dispersion of probability distribution. The population variance of a random variable X is Var(X) = E[(X − E[X])²], where E denotes expected value. The sample variance of a set of N observations {x_i}, i = 1, 2,…, N, is given by $V = \frac{1}{N} \sum_{i = 1}^{N} {(x_{i} - μ)}^{2},$ where μ‎ is the sample mean. See also covariance matrix.
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