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Variance—Wolfram Language Documentation

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• See Also
  • StandardDeviation
  • Covariance
  • Correlation
  • TrimmedVariance
  • WinsorizedVariance
  • BiweightMidvariance
  • QnDispersion
  • SnDispersion
  • Mean
  • MeanDeviation
  • MedianDeviation
  • Kurtosis
  • CentralMoment
  • Expectation
• Related Guides
  • Descriptive Statistics
  • Statistical Data Analysis
  • GPU Computing
  • Math & Counting Operations on Lists
  • Time Series Processing
  • Statistical Moments and Generating Functions
  • Numerical Data
  • Scientific Data Analysis
  • Precollege Education
  • Image Processing & Analysis
  • Finite Mathematics
  • Probability & Statistics
  • GPU Computing with Apple
  • GPU Computing with NVIDIA
  • Date & Time
  • Signal Visualization & Analysis
  • Audio Processing
  • Symbolic Vectors, Matrices and Arrays
• Tech Notes
  • Basic Statistics
  • Descriptive Statistics
  • Discrete Distributions
  • Continuous Distributions

Variance[data]

gives the variance estimate of the elements in data.

Variance[dist]

gives the variance of the distribution dist.

• Variance measures dispersion of data or distributions.
• Variance[data] gives the unbiased estimate of variance.
• For VectorQ data , the variance estimate is given by for reals and for complexes and =Mean[data].
• For MatrixQ data, the variance estimate is computed for each column vector, with Variance[{{x₁,y₁,…},{x₂,y₂,…},…}] equivalent to {Variance[{x₁,x₂,…}],Variance[{y₁,y₂,…}]}. »
• For ArrayQ data, variance is equivalent to ArrayReduce[Variance,data,1]. »
• For a real weighted WeightedData[{x₁,x₂,…},{w₁,w₂,…}], the variance is given by . »
• Variance handles both numerical and symbolic data.
• The data can have the following additional forms and interpretations:
• For a univariate distribution dist, the variance is given by σ²=Expectation[(x-μ)²,xdist] with μ=Mean[dist]. »
• For a multivariate distribution dist, the variance is given by {σ_x²,σ_y²,…}=Expectation[{(x-μ_x)²,(y-μ_y)²,…},{x,y,…}dist]. »
• For a random process proc, the variance function can be computed for slice distribution at time t, SliceDistribution[proc,t], as σ[t]²=Variance[SliceDistribution[proc,t]]. »

Variance of a list of numbers:

Variance of elements in each column:

Variance of a list of dates:

Variance of a parametric distribution:

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:

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:

Channelwise variance of an RGB image:

Variance of a grayscale image:

On audio objects, Variance works channelwise:

Compute variance of dates:

Compute the weighted variance of dates:

Compute the variance of dates given in different calendars:

Compute the variance of times:

Compute the variance of times with different time zone specifications:

Find the variance for univariate distributions:

Multivariate distributions:

Variance for derived distributions:

Data distribution:

Variance function for a random process:

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:

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

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