Variance

Variance[data]

gives the variance estimate of the elements in data.

Variance[dist]

gives the variance of the distribution dist.

Details

Examples

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Basic Examples  (3)

Variance of a list of numbers:

Variance of elements in each column:

Variance of a parametric distribution:

Scope  (17)

Basic Uses  (7)

Exact input yields exact output:

Approximate input yields approximate output:

Find the variance of WeightedData:

Find the variance of EventData:

Find the variance of TemporalData:

Find the variance of a TimeSeries:

The variance depends only on the values:

Find the variance of data involving quantities:

Array Data  (5)

Variance for a matrix gives columnwise variances:

Variance for a tensor gives columnwise variances at the first level:

Works with large arrays:

When the input is an Association, Variance works on its values:

SparseArray data can be used just like dense arrays:

Find the variance of a QuantityArray:

Image and Audio Data  (2)

Channelwise variance of an RGB image:

Variance of a grayscale image:

On audio objects, Variance works channelwise:

Distributions and Processes  (3)

Find the variance for univariate distributions:

Multivariate distributions:

Variance for derived distributions:

Data distribution:

Variance function for a random process:

Applications  (5)

Variance is a measure of dispersion:

Compute a moving variance for samples of three random processes:

Compare data volatility by smoothing with moving variance:

Find the mean and variance for the number of great inventions and scientific discoveries in each year from 1860 to 1959:

Investigate weak stationarity of the process data by analyzing variance of slices:

Use a larger plot range to see how relatively small the variations are:

Find the variance of the heights for the children in a class:

Properties & Relations  (11)

The square root of Variance is StandardDeviation:

Variance is a scaled squared Norm of deviations from the Mean:

Variance is a scaled CentralMoment:

The square root of Variance is a scaled RootMeanSquare of the deviations:

Variance is a scaled Mean of squared deviations from the Mean:

Variance is a scaled SquaredEuclideanDistance from the Mean:

Variance is less than MeanDeviation if all absolute deviations are less than 1:

Variance is greater than MeanDeviation if all absolute deviations are greater than 1:

Variance of a random variable as an Expectation:

Variance gives an unbiased sample estimate:

Unbiased means that the expected value of the sample variance with respect to the population distribution equals the variance of the underlying distribution:

Variance gives an unbiased weighted sample estimate:

Unbiased means that the expected value of the sample variance with respect to the population distribution equals the variance of the underlying distribution:

Neat Examples  (1)

The distribution of Variance estimates for 20, 100, and 300 samples:

Wolfram Research (2003), Variance, Wolfram Language function, https://reference.wolfram.com/language/ref/Variance.html (updated 2023).

Text

Wolfram Research (2003), Variance, Wolfram Language function, https://reference.wolfram.com/language/ref/Variance.html (updated 2023).

CMS

Wolfram Language. 2003. "Variance." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/Variance.html.

APA

Wolfram Language. (2003). Variance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Variance.html

BibTeX

@misc{reference.wolfram_2023_variance, author="Wolfram Research", title="{Variance}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/Variance.html}", note=[Accessed: 21-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_variance, organization={Wolfram Research}, title={Variance}, year={2023}, url={https://reference.wolfram.com/language/ref/Variance.html}, note=[Accessed: 21-April-2024 ]}