# standard deviation

## standard deviation

noun Statistics.
a measure of dispersion in a frequency distribution, equal to the square root of the mean of the squares of the deviations from the arithmetic mean of the distribution.

Origin:
1920–25

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World English Dictionary
 standard deviation —n statistics a measure of dispersion obtained by extracting the square root of the mean of the squared deviations of the observed values from their mean in a frequency distribution

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
Medical Dictionary

standard deviation n.
Symbol σ
A statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.

The American Heritage® Stedman's Medical Dictionary
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American Heritage
Science Dictionary
 standard deviation   (stān'dərd)  Pronunciation Key  A statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.
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American Heritage
Cultural Dictionary

### standard deviation definition

In statistics, a measure of how much the data in a certain collection are scattered around the mean. A low standard deviation means that the data are tightly clustered; a high standard deviation means that they are widely scattered.

Note: About sixty-eight percent of the data are within one standard deviation of the mean.
The American Heritage® New Dictionary of Cultural Literacy, Third Edition
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FOLDOC
Computing Dictionary

### standard deviation definition

statistics
(SD) A measure of the range of values in a set of numbers. Standard deviation is a statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.
The standard deviation of a random variable or list of numbers (the lowercase greek sigma) is the square of the variance. The standard deviation of the list x1, x2, x3...xn is given by the formula:
sigma = sqrt(((x1-(avg(x)))^2 + (x1-(avg(x)))^2 + ... + (xn(avg(x)))^2)/n)
The formula is used when all of the values in the population are known. If the values x1...xn are a random sample chosen from the population, then the sample Standard Deviation is calculated with same formula, except that (n-1) is used as the denominator.
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["Barrons Dictionary of Mathematical Terms, second edition"].
(2003-05-06)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Encyclopedia Britannica
Encyclopedia

standard deviation

in statistics, a measure of the variability (dispersion or spread) of any set of numerical values about their arithmetic mean (average; denoted by mu). It is specifically defined as the positive square root of the variance (sigma2); in symbols, sigma2=Sigma(xImu)2/n, where Sigma is a compact notation used to indicate that as the index (I) changes from 1 to n (the number of elements in the data set), the square of the difference between each element xI and the mean, divided by n, is calculated and these values are added together.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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Example sentences
The standard deviation is essentially the average difference between each data
point and the average.
In the game probability model, this roughly translates into a standard
deviation below average.
But over ten-year holding periods the standard deviation drops to five
percentage points.
The main arguments it takes are the average and the standard deviation of the
distribution you want.
Synonyms