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Statistics[Variance] - compute the variance
Calling Sequence
Variance(A, ds_options)
Variance(X, rv_options)
Parameters
A
-
list, rtable, or Array of real constants, or Matrix data set; data set
X
algebraic; random variable or distribution
ds_options
(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the variance of a data set
rv_options
(optional) equation of the form numeric=value; specifies options for computing the variance of a random variable
Description
The Variance function computes the sample variance of the specified data set or random variable. In the data set case the following (unbiased) estimate for the variance is used:
where N is the number of elements per data set A.
The first parameter can be a data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
Computation
By default, all computations involving random variables are performed symbolically (see option numeric below).
All computations involving data are performed in floating-point; therefore, all data provided must have type/realcons and all returned solutions are floating-point, even if the problem is specified with exact values.
For more information about computation in the Statistics package, see the Statistics[Computation] help page.
Data Set Options
The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.
ignore=truefalse -- This option controls how missing data is handled by the Variance command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Variance command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.
weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight .
Random Variable Options
The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.
numeric=truefalse -- By default, the variance is computed using exact arithmetic. To compute the variance numerically, specify the numeric or numeric = true option.
Compatibility
The A parameter was updated in Maple 16.
Examples
Compute the variance of the beta distribution with parameters and .
Use numeric parameters.
Generate a random sample of size 100000 drawn from the above distribution and compute the sample variance.
Compute the standard error of the sample variance for the normal distribution with parameters 5 and 2.
Create a beta-distributed random variable and compute the variance of .
Verify this using simulation.
Compute the variance of a weighted data set.
Consider the following Matrix data set.
We compute the variance of each of the columns.
See Also
Statistics, Statistics[Computation], Statistics[DescriptiveStatistics], Statistics[Distributions], Statistics[ExpectedValue], Statistics[RandomVariables], Statistics[StandardError]
References
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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