The Variation function computes the coefficient of variation of the specified random variable or data set.

The first parameter can be a data set (e.g., a Vector), a Matrix data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

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.

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 Variation command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Variation 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 $1$.

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 coefficient of variation is computed using exact arithmetic. To compute the coefficient of variation numerically, specify the numeric or numeric = true option.

with(Statistics):

Variation('Beta'(p, q));

$\frac{\sqrt{\frac{pq}{p+q+1}}}{p}$

Variation('Beta'(3, 5));

$\frac{\sqrt{15}}{9}$

Variation('Beta'(3, 5), numeric);

$0.4303314828$

A := Sample('Beta'(3, 5), 10^5):

Variation(A);

$0.432422803985375$

X := RandomVariable(Normal(5, 2)):

B := Sample(X, 10^6):

[Variation(X), StandardError[10^6](Variation, X)];

$\left[\frac{2}{5}\,\frac{\sqrt{29}}{12500}\right]$

Variation(B);

$0.400136408914884$

V := <seq(i, i = 57..77), undefined>:

W := <2, 4, 14, 41, 83, 169, 394, 669, 990, 1223, 1329, 1230, 1063, 646, 392, 202, 79, 32, 16, 5, 2, 5>:

Variation(V, weights = W);

$Float\left(\mathrm{undefined}\right)$

Variation(V, weights = W, ignore = true);

$0.0406951177946295$

M := Matrix([[3,1130,114694],[4,1527,127368],[3,907,88464],[2,878,96484],[4,995,128007]]);

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

Variation(M);

$\left[\begin{array}{ccc}0.261456258291899& 0.243306895704371& 0.161742551310824\end{array}\right]$

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

The A parameter was updated in Maple 16.