The Quartile function computes the specified quartile 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]).

The second parameter q is the quartile.

For a description of the available options, see the Statistics[Quantile] help page. Calling Quartile with quartile $q$ is equivalent to calling Quantile with probability $0.25q$.

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

$\mathrm{Quartile}\left(\mathrm{Weibull}\left(a\,b\right)\,3\right)$

$a{\left(2\ln \left(2\right)\right)}^{\frac{1}{b}}$

$\mathrm{Quartile}\left(\mathrm{Weibull}\left(3\,5\right)\,3\right)$

$32^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}{\ln \left(2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}$

$\mathrm{Quartile}\left(\mathrm{Weibull}\left(3\,5\right)\,3\,\mathrm{numeric}\right)$

$3.20252365335208$

$A≔\mathrm{Sample}\left(\mathrm{Weibull}\left(3\,5\right)\,{10}^5\right)\:$

$\mathrm{Quartile}\left(A\,3\right)$

$3.20252404724559$

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

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

$\mathrm{Quartile}\left(M\,3\right)$

$\left[\begin{array}{ccc}4.& 1262.33333333333& 127581.\end{array}\right]$

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.