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## standard deviation

A measure of the dispersion of data in statistics. For a set of values a 1, a 2, a 3, … an , the mean m is given by (a 1 + a ...

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### A Dictionary of Geology and Earth Sciences (5 ed.)

Reference type:
Subject Reference
Current Version:
2020

... deviation 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...

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### A Dictionary of Dentistry (2 ed.)

Reference type:
Subject Reference
Current Version:
2020
Subject:
Medicine and health, Dentistry
Length:
43 words

... deviation (in statistics) A measure of the range of variation from an average of a group of measurements. 68% of all measurements fall within one standard deviation of the mean . 95% of all measurements fall within two standard deviations of the...

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### A Dictionary of Zoology (5 ed.)

Reference type:
Subject Reference
Current Version:
2020
Subject:
Science and technology, Life Sciences
Length:
69 words

... deviation ( σ ‎ ) A measure of the normal variation of a set of data. In any given measurement, two-thirds of the data 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. https://www.mathsisfun.com/data/standard-deviation.html Description of standard deviation and...

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### The Concise Oxford Dictionary of Archaeology (2 ed.)

Reference type:
Subject Reference
Current Version:
2009
Subject:
Archaeology, History
Length:
63 words

... deviation [Ge] A measure of the distribution around the mean of a group of defined values. Normally, the values of 68 per cent of cases fall within one standard deviation of the mean, 95 per cent between two, and 99 per cent within three standard deviations either side of the mean. Standard deviation is usually expressed as a plus or negative...

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### Dictionary of the Social Sciences

Reference type:
Subject Reference
Current Version:
2002
Subject:
Social sciences
Length:
123 words

... deviation and standard error A statistical measure, standard deviation describes the degree of deviation of a set of values in a distribution from the mean of those values. In statistical terms, it is calculated by adding up the square of the deviation of each individual value (a total known as the sum of squares or SSTO) and dividing by the number of values in order to obtain an average. This is known as the variance . Where all values are equal, the variance is zero. The standard deviation is obtained by taking the square root of the...

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### A Dictionary of Genetics (8 ed.)

Reference type:
Subject Reference
Current Version:
2014
Subject:
Science and technology, Life Sciences
Length:
65 words

... deviation ( s ) a measure of the variability in a population of items. The standard deviation of a sample is given by the equation where N is the number of items in the sample and Σ(x − x-x̄) 2 is the sum of the squared deviations of each measurement from the mean...

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### A Dictionary of Mechanical Engineering (2 ed.)

Reference type:
Subject Reference
Current Version:
2019

...standard deviation ( σ ‎ ) The square root of variance , a measure of the spread of data about the mean value . See also root-mean square...

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### A Dictionary of Statistics (3 ed.)

Reference type:
Subject Reference
Current Version:
2014

... deviation ( sd ) The square root of the variance . Karl Pearson introduced the term in 1893 , using the symbol σ in the following...

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### The Oxford Dictionary of Sports Science & Medicine (3 ed.)

Reference type:
Subject Reference
Current Version:
2007

... deviation A statistical index of the variability of data within a distribution. It is the square root of the average of the squared deviation from the mean; that is, it equals the square root of the variance. See also descriptive statistics...

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### A Dictionary of Economics (5 ed.)

Reference type:
Subject Reference
Current Version:
2017
Subject:
Social sciences, Economics
Length:
45 words

...standard deviation 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...

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### World Encyclopedia

Reference type:
Subject Reference
Current Version:
2004
Subject:
Encyclopedias
Length:
73 words

... deviation ( symbol σ or s ) In statistics, a measure of deviation of observed data or scores from the mean . A small standard deviation indicates that observations cluster around the mean, while a large one indicates that the data are spread far from the mean. The standard deviation is equal to the square root of the variance (the mean of the sum of the squared differences of the data points from the...

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### The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

... deviation 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 , σ 2 ), with mean μ and standard deviation σ , approximately 95% of the distribution lies in the interval between μ −2 σ and μ +2 σ . The standard deviation of an estimator of a population parameter is the standard error...

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### A Dictionary of Finance and Banking (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

... deviation A measure of the dispersion of statistical data. For a series of n values x 1 , x 2 , x n , it is given by the formula where x is the average of the n values. The standard deviation of the returns from an investment can be used as a measure of the risk associated with that...

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### A Dictionary of Business and Management (6 ed.)

Reference type:
Subject Reference
Current Version:
2016
Subject:
Length:
74 words
Illustration(s):
1

... deviation A measure of the dispersion of statistical data. For a series of n values x 1 , x 2 , x n , it is given by the formula √ [ ( 1 / n ) ∑ ( x i − x ) ] where x is the average of the n values. The standard deviation of the returns from an investment can be used as a measure of the risk associated with that...

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### A Dictionary of Finance and Banking (6 ed.)

Reference type:
Subject Reference
Current Version:
2018
Subject:
Social sciences, Business and Management, Economics
Length:
74 words
Illustration(s):
1

... deviation A measure of the dispersion of statistical data. For a series of n values x 1 , x 2 , x n , it is given by the formula √ [ ( 1 / n ) ∑ ( x i - x ) ] where x is the average of the n values. The standard deviation of the returns from an investment can be used as a measure of the risk associated with that...

## standard deviation Reference library

### The Handbook of International Financial Terms

Reference type:
Subject Reference
Current Version:
2005
Subject:
Social sciences, Business and Management, Economics
Length:
124 words
Illustration(s):
2

... deviation . A measure of the dispersion of a distribution and therefore a useful measure of its risk . The square root of the variance is more intelligible than the variance since it is expressed in the same units as the distribution. If the data is normally distributed, then two-thirds of the observations will lie within plus or minus one standard deviation of the mean; and 99.7% within plus or minus three standard deviations. The general formula is: where σ is the standard deviation; n the number of observations; ρ i the probability of the i th...

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### A Dictionary of Chemical Engineering

Reference type:
Subject Reference
Current Version:
2014
Subject:
Science and technology, Engineering and Technology
Length:
108 words
Illustration(s):
1

...standard deviation (Symbol σ) 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 = ∑ i = 1 n ( x i − x − ) 2 n − 1 where 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. ...

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### A Dictionary of Biology (8 ed.)

Reference type:
Subject Reference
Current Version:
2019
Subject:
Science and technology, Life Sciences
Length:
130 words

...standard deviation ( SD ) In statistics, a measure of the dispersion of data about the mean. For a set of values a 1 , a 2 , a 3 ,… a n , the mean m is given by ( a 1 + a 2 +…+ a n )/ n . The deviation of each value is the absolute value of the difference from the mean #| m − a 1 #|, etc. The standard deviation is the square root of the mean of the squares of these values, i.e. √[(#| m − a 1 #| 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...

## standard deviation ((in statistics)) Quick reference

### Concise Medical Dictionary (10 ed.)

Reference type:
Subject Reference
Current Version:
2020
Subject:
Medicine and health, Clinical Medicine
Length:
124 words

...A large standard deviation indicates that data points vary across a wide range of values, whereas a small standard deviation indicates the opposite. See also significance...

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### A Dictionary of Physics (8 ed.)

Reference type:
Subject Reference
Current Version:
2019
Subject:
Science and technology, Physics
Length:
118 words
Illustration(s):
1

...standard deviation A measure of the dispersion of data in statistics. For a set of values a 1 , a 2 , a 3 ,…, a n , the mean m is given by ( a 1 + a 2 +…+ a n )/ n . The deviation of each value is the absolute value of the difference from the mean, i.e. | m − a 1 |, etc. The standard deviation is the square root of the mean of the squares of these values, i.e. √ [ ( | m - a 1 | 2 + … + | m - a n | 2 ) / n ] When the data are continuous the sum is replaced by an integral....

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