In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.
Standard deviation definition formula
The standard deviation is the square root of the variance of random variable X, with mean value of μ.
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From the definition of the standard deviation we can get:
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Standard deviation of continuous random variable
For continuous random variable with mean value μ and probability density function f(x):
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or:
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Standard deviation of discrete random variable
For discrete random variable X with mean value μ and probability mass function P(x):
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or:
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