Standard Deviation

Explained:

standard deviation

variance


Variance is a parameter that measures how dispersed a random variable's probability distribution is. In Exhibit 1, probability density functions (PDFs) are indicated for two random variables. The one on the left is more dispersed than the one on the right. It has a higher variance.

High vs. Low Variance
Exhibit 1

These graphs illustrate the notion of variance. The one on the left is more dispersed than the one on the right. It has a higher variance.

The variance of a random variable X, denoted 2 or var(X), is defined as the expectation of a particular function of X:

var(X) = E[(X m)2]

[1]

where = E(X). Standard deviation, denoted or std(X), is the positive square root of variance.

   

Related Internal Links

expected value A parameter describing the "center of gravity" of a distribution.

kurtosis A parameter describing the peakedness and tails of a distribution.

linear polynomial of a random vector A random variable or random vector that is defined as a linear polynomial of a random vector.

normal distribution A continuous probability distribution whose probability density function has a "bell" shape.

quantile A notion from probability that can be used as a parameter.

skewness A parameter that describes the lack of symmetry of a distribution.

uniform distribution A continuous probability distribution that has constant probability on a finite interval.

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