Range - Maple Help

Statistics

 Range
 compute the range

 Calling Sequence Range(A, options)

Parameters

 A - options - (optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the range of a data set

Description

 • The Range function computes the range of the specified data set, which is defined as the difference between the largest and the smallest values. Note that the range is based only on the lowest and highest extreme values in the sample. Use the Support command to compute the support set of a random variable.
 • The first parameter can be a one-dimensional data set (given as e.g. a Vector) or a Matrix data set.

Computation

 • 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.

Options

 The 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 Range command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Range 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 $1$. This options is added for consistency only as adding weights to the data does not affect the range.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$

Generate a random sample of size 100000 drawn from the Rayleigh distribution and compute the sample range.

 > $A≔\mathrm{Sample}\left(\mathrm{Rayleigh}\left(3\right),{10}^{5}\right):$
 > $\mathrm{Range}\left(A\right)$
 ${13.8294890185824}$ (1)

Compute the range of a data set with missing values.

 > $V≔⟨\mathrm{seq}\left(i,i=57..77\right),\mathrm{undefined}⟩:$
 > $W≔⟨\mathrm{seq}\left(1,i=1..22\right)⟩:$
 > $\mathrm{Range}\left(V\right)$
 ${Float}{}\left({\mathrm{undefined}}\right)$ (2)
 > $\mathrm{Range}\left(V,\mathrm{ignore}=\mathrm{true}\right)$
 ${20.}$ (3)
 > $\mathrm{Range}\left(V,\mathrm{weights}=W,\mathrm{ignore}=\mathrm{true}\right)$
 ${20.}$ (4)

Consider the following Matrix data set.

 > $M≔\mathrm{Matrix}\left(\left[\left[3,1130,114694\right],\left[4,1527,127368\right],\left[3,907,88464\right],\left[2,878,96484\right],\left[4,995,128007\right]\right]\right)$
 ${M}{≔}\left[\begin{array}{ccc}{3}& {1130}& {114694}\\ {4}& {1527}& {127368}\\ {3}& {907}& {88464}\\ {2}& {878}& {96484}\\ {4}& {995}& {128007}\end{array}\right]$ (5)

We compute the range of each of the columns.

 > $\mathrm{Range}\left(M\right)$
 $\left[\begin{array}{ccc}{2.}& {649.}& {39543.}\end{array}\right]$ (6)

References

 Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

 • The A parameter was updated in Maple 16.