Standard deviation


Standard Deviation (or standard deviation) is the square root of the variance. Standard deviation characterizes the dispersion of a feature - the larger the standard deviation, the greater the dispersion of feature values.

Formula for Standard Deviation

$$\sigma=\sqrt{D(X)}=\sqrt{E(X-E(X))^{2}}$$

where,

E(X)— mean of the random variable X.

The standard deviation of a finite sequence of numbers can be expressed by the formula:

$$\sigma=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}$$

where,

— mean of random variables xi.

The sample standard deviation can be expressed by the formula (Bessel's correction):

$$\sigma=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}$$

where,

— mean of random variables xi.

See also:


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