“standard deviation”的概念、定义、翻译、参考文献-科学参考

standard deviation

Physics

A measure of the dispersion of data in statistics. For a set of values a₁, a₂, a₃,…, a_n, the mean m is given by (a₁+a₂+…+a_n)/n. The deviation of each value is the absolute value of the difference from the mean, i.e. |m−a₁|, etc. The standard deviation is the square root of the mean of the squares of these values, i.e.

$\sqrt [(| m - a_{1} |^{2} + … + | m - a_{n} |^{2}) / n]$

When the data are continuous the sum is replaced by an integral.

Mathematics

The positive square root of the variance, a commonly used measure of the dispersion of observations in a sample. For a normal distribution N(μ‎,σ‎²), with mean μ‎ and standard deviation σ‎, approximately 95% of the distribution lies in the interval between μ‎−2σ‎ and μ‎+2σ‎.

The standard deviation of an estimator of a population parameter is the standard error.

Statistics

The square root of the variance. Karl Pearson introduced the term in 1893, using the symbol σ in the following year.

Chemical Engineering

A statistical measure of the dispersion of a set of data from the mean and equal to the square root of the variance. In a sample of n observations, the standard deviation is:
$σ = \sqrt{\frac{{\sum_{i = 1}^{n} (x_{i} - \bar{x})}^{2}}{n - 1}}$

(p. 356) where $\bar{x}$ is the mean of the sample. The standard deviation is therefore the square root of the mean of the sum of squared differences of the data points from the mean. A small value indicates a cluster around the mean whereas a large value indicates a wider spread of data.

Computer

See measures of variation.

Electronics and Electrical Engineering

In statistics, a measure of the degree to which sample data is spread about the mean of that data. It is computed as the square root of the variance, which is the sum of the squares of the difference between each data-point and the average.
$σ = \sqrt{\sum_{i = 1}^{n} {(x_{i} - μ)}^{2}}$
Here μ is the mean, n is the number of data items, x_i is the ith data item, and σ is the standard deviation.

Biology

In statistics, a measure of the dispersion of data about the mean. For a set of values a₁, a₂, a₃,…a_n, the mean m is given by (a₁+a₂+…+a_n)/n. The deviation of each value is the absolute value of the difference from the mean #|m−a₁#|, etc. The standard deviation is the square root of the mean of the squares of these values, i.e. √[(#|m−a₁#|² +…#|m−a_n#|²)/n]. A large standard deviation indicates that data points vary across a wide range of values, whereas a small SD indicates the opposite. See also distribution; significance.

Geology and Earth Sciences

A measure of the normal variation within a set of data. In any given measurement, two-thirds of the samples fall within one standard deviation on either side of the mean, 95% between two standard deviations, and so on; the proportion falls off sharply because of the bell-curve effect. The standard deviation is calculated as the root-mean-square deviation.

Economics

In a sample of observations, a commonly used measure of dispersion, defined as the square root of the average of squared deviations of the observations from the sample mean. In a population, the square root of the variance of the distribution.

单词	standard deviation
释义	standard deviation Physics A measure of the dispersion of data in statistics. For a set of values a₁, a₂, a₃,…, a_n, the mean m is given by (a₁+a₂+…+a_n)/n. The deviation of each value is the absolute value of the difference from the mean, i.e. \|m−a₁\|, etc. The standard deviation is the square root of the mean of the squares of these values, i.e. $\sqrt [(\| m - a_{1} \|^{2} + … + \| m - a_{n} \|^{2}) / n]$ When the data are continuous the sum is replaced by an integral. Mathematics The positive square root of the variance, a commonly used measure of the dispersion of observations in a sample. For a normal distribution N(μ‎,σ‎²), with mean μ‎ and standard deviation σ‎, approximately 95% of the distribution lies in the interval between μ‎−2σ‎ and μ‎+2σ‎. The standard deviation of an estimator of a population parameter is the standard error. Statistics The square root of the variance. Karl Pearson introduced the term in 1893, using the symbol σ in the following year. Chemical Engineering A statistical measure of the dispersion of a set of data from the mean and equal to the square root of the variance. In a sample of n observations, the standard deviation is: $σ = \sqrt{\frac{{\sum_{i = 1}^{n} (x_{i} - \bar{x})}^{2}}{n - 1}}$ (p. 356) where $\bar{x}$ is the mean of the sample. The standard deviation is therefore the square root of the mean of the sum of squared differences of the data points from the mean. A small value indicates a cluster around the mean whereas a large value indicates a wider spread of data. Computer See measures of variation. Electronics and Electrical Engineering In statistics, a measure of the degree to which sample data is spread about the mean of that data. It is computed as the square root of the variance, which is the sum of the squares of the difference between each data-point and the average. $σ = \sqrt{\sum_{i = 1}^{n} {(x_{i} - μ)}^{2}}$ Here μ is the mean, n is the number of data items, x_i is the ith data item, and σ is the standard deviation. Biology In statistics, a measure of the dispersion of data about the mean. For a set of values a₁, a₂, a₃,…a_n, the mean m is given by (a₁+a₂+…+a_n)/n. The deviation of each value is the absolute value of the difference from the mean #\|m−a₁#\|, etc. The standard deviation is the square root of the mean of the squares of these values, i.e. √[(#\|m−a₁#\|² +…#\|m−a_n#\|²)/n]. A large standard deviation indicates that data points vary across a wide range of values, whereas a small SD indicates the opposite. See also distribution; significance. Geology and Earth Sciences A measure of the normal variation within a set of data. In any given measurement, two-thirds of the samples fall within one standard deviation on either side of the mean, 95% between two standard deviations, and so on; the proportion falls off sharply because of the bell-curve effect. The standard deviation is calculated as the root-mean-square deviation. Economics In a sample of observations, a commonly used measure of dispersion, defined as the square root of the average of squared deviations of the observations from the sample mean. In a population, the square root of the variance of the distribution.
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