Statistics[Variance] - compute the variance
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Calling Sequence
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Variance(A, ds_options)
Variance(X, rv_options)
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Parameters
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A
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list, rtable, or Array of real constants, or Matrix data set; data set
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X
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algebraic; random variable or distribution
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ds_options
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(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
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rv_options
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(optional) equation of the form numeric=value; specifies options for computing the variance of a random variable
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Description
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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:
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where N is the number of elements per data set A.
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Computation
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By default, all computations involving random variables are performed symbolically (see option numeric below).
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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.
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Data Set Options
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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.
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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.
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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 .
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Random Variable Options
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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.
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numeric=truefalse -- By default, the variance is computed using exact arithmetic. To compute the variance numerically, specify the numeric or numeric = true option.
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Compatibility
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The A parameter was updated in Maple 16.
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Examples
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Compute the variance of the beta distribution with parameters and .
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Use numeric parameters.
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Generate a random sample of size 100000 drawn from the above distribution and compute the sample variance.
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Compute the standard error of the sample variance for the normal distribution with parameters 5 and 2.
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Create a beta-distributed random variable and compute the variance of .
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Verify this using simulation.
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Compute the variance of a weighted data set.
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Consider the following Matrix data set.
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We compute the variance of each of the columns.
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References
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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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Download Help Document
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