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,
x̄— 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,
x̄— mean of random variables xi.
See also:
FAQ
What is standard deviation?
It measures how spread out values are around the mean.
How is it related to variance?
Standard deviation is the square root of variance.
Why use sample standard deviation?
Sample standard deviation uses Bessel's correction when data is only a sample of a larger population.
