Standard deviation

In probability and statistics, the standard deviation is the most commonly used measure of statistical dispersion. Simply put, it measures how spread out the values in a data set are.

Related Topics:
Probability - Statistics - Statistical dispersion

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The importance of the standard deviation arises from Chebyshev's theorem, which asserts that in any data set, nearly all of the values will be close to the mean value, where the meaning of "close to" is specified by the standard deviation.

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The standard deviation is defined as the square root of the variance. This means it is the root mean square (RMS) deviation from the average. It is defined this way in order to give us a measure of dispersion that is (1) a non-negative number, and (2) has the same units as the data. For example, if the data are distance measurements in meters, the standard deviation will also be measured in meters.

Related Topics:
Square root - Variance - Root mean square

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A distinction is made between the standard deviation σ (sigma) of a whole population or of a random variable, and the standard deviation s of a subset-population sample. The formulae are given below.

Related Topics:
Sigma - Population - Random variable - Sample

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The term standard deviation was introduced to statistics by Karl Pearson (On the dissection of asymmetrical frequency curves, 1894).

Related Topics:
Karl Pearson - 1894

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