What is Variance: Definition and 356 Discussions

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. In other words, it measures how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by




σ

2




{\displaystyle \sigma ^{2}}
,




s

2




{\displaystyle s^{2}}
, or



Var
⁡
(
X
)


{\displaystyle \operatorname {Var} (X)}
.

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