Standard Deviation

Standard deviation is the square root of the variance, i.e. the square root of the mean of the squares of the deviations from the mean value of a vibrating quantity. The square of the standard deviation is the variance. An expression of the so-called "second moment," which describes the "dispersion" or variability around the mean.

In noise data, the standard deviation should be approximately the same as the rms.

for the data series: x1, x2, x3,....,xn the standard deviation of a sample, σ is:

The standard deviation of the entire population, σp
Represents about the same likelihood of tossing a coin and getting more than eight heads in a row.
The level of certainty required in Particle Physics for a "discovery".
Corresponds to tossing a coin and getting more than 20 heads in a row.

See also: Average Deviation, Mean, Normal Distribution, Relative Standard Deviation, Standard Error, Statistic, Variance.

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Subjects: Statistics