# Variance

The variance of a random variable or distribution is the expectation, or mean, of the squared deviation of that variable from its expected value or mean. Thus the variance is a measure of the amount of variation of the values of that variable, taking account of all possible values and their probabilities or weightings (not just the extremes which give the range).

For example, a perfect six-sided die, when thrown, has expected value of

Its expected absolute deviation—the mean of the equally likely absolute deviations from the mean—is

But its expected squared deviation—its variance (the mean of the equally likely squared deviations)—is

As another example, if a coin is tossed twice, the number of heads is: 0 with probability 0.25, 1 with probability 0.5 and 2 with probability 0.25. Thus the expected value of the number of heads is:

and the variance is:

### Other articles related to "variance":

Squared Deviations
... theory and statistics, the definition of variance is either the expected value (when considering a theoretical distribution), or average value (for actual experimental data), of squared deviations from the mean ... Computations for analysis of variance involve the partitioning of a sum of squared deviations ... for a random variable with mean and variance Therefore From the above, the following are easily derived If is a vector of n predictions, and is the vector of the true values, then the SSE of the ...
Estimation - Corrected Sample Standard Deviation
... When discussing the bias, to be more precise, the corresponding estimator for the variance, the biased sample variance equivalently the second central moment of the sample (as the mean is the first ... The bias in the variance is easily corrected, but the bias from the square root is more difficult to correct, and depends on the distribution in question ... An unbiased estimator for the variance is given by apply Bessel's correction, using N − 1 instead of N to yield the unbiased sample variance, denoted s2 This estimator is unbiased if the variance exists and the ...
Variance - Moment of Inertia
... The variance of a probability distribution is analogous to the moment of inertia in classical mechanics of a corresponding mass distribution along a line, with respect to rotation about its center of mass ... because of this analogy that such things as the variance are called moments of probability distributions ... The covariance matrix might look like That is, there is the most variance in the x direction ...
Sample Standard Deviation - Rapid Calculation Methods
... It has been suggested that this article be merged into Algorithms for calculating variance ... This is a "one pass" algorithm for calculating variance of n samples without the need to store prior data during the calculation ... n where A is the mean value Sample variance Population variance ...
Situations Where Spot Zoning May Arise - Variance
... A variance is the license to deviate from the land-use restrictions imposed by the zoning ordinance ... A variance usually requires the landowner suffer a substantial hardship which only the granting of a variance may remedy ... If a local zoning authority decides to grant a variance to a landowner who lacks substantial hardship, then its legality (regarding equal protection) may be called into question ...

### Famous quotes containing the word variance:

There is an untroubled harmony in everything, a full consonance in nature; only in our illusory freedom do we feel at variance with it.
Fyodor Tyutchev (1803–1873)