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Statistics

 Tally
 compute absolute frequencies

 Calling Sequence Tally(X, options)

Parameters

 X - options - (optional) equation(s) of the form option=value where option is one of weights or output; specify options for the Tally function

Description

 • The Tally function returns a table of distinct elements in X together with their frequencies. (See also Statistics[TallyInto]).
 • The first parameter X is the data set, given as e.g. a Vector.

Options

 The options argument can contain one or more of the options shown below.
 • output=list or table -- Set the type of output returned. The default value is list. In either case, the output consists of equations of the form element=frequency.
 • weights=Array or list -- A vector of weights (one dimensional rtable). If weights are given, the Tally function will return distinct elements in X paired with their cumulative weights. Note that the weights provided must have type[realcons] and the returned frequencies are floating-point, even if the problem is specified with exact values. Both the data array and the weights array must have the same number of elements.

Notes

 • If the value of the output option is set to output=list, the order of elements in the list is session dependent.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $A≔\mathrm{Array}\left(\left[3,3,3,1,1,a,b,b,a,a,a,a,\mathrm{π},\mathrm{π},\mathrm{π},\mathrm{π}\right]\right)$
 ${A}{:=}\left[\begin{array}{c}{\mathrm{1 .. 16}}{\mathrm{Array}}\\ {\mathrm{Data Type:}}{\mathrm{anything}}\\ {\mathrm{Storage:}}{\mathrm{rectangular}}\\ {\mathrm{Order:}}{\mathrm{Fortran_order}}\end{array}\right]$ (1)
 > $\mathrm{Tally}\left(A\right)$
 $\left[{1}{=}{2}{,}{3}{=}{3}{,}{\mathrm{π}}{=}{4}{,}{b}{=}{2}{,}{a}{=}{5}\right]$ (2)
 > $\mathrm{Tally}\left(A,\mathrm{output}=\mathrm{table}\right)$
 ${\mathrm{table}}\left(\left[{1}{=}{2}{,}{3}{=}{3}{,}{\mathrm{π}}{=}{4}{,}{b}{=}{2}{,}{a}{=}{5}\right]\right)$ (3)
 > $C≔\mathrm{Array}\left(\left[3,3,1,a,b,\mathrm{π}\right]\right)$
 ${C}{:=}\left[\begin{array}{cccccc}{3}& {3}& {1}& {a}& {b}& {\mathrm{π}}\end{array}\right]$ (4)
 > $W≔\mathrm{Array}\left(\left[0.25,0.5,0.125,0.5,0.375,0.5625\right]\right)$
 ${W}{:=}\left[\begin{array}{cccccc}{0.25}& {0.5}& {0.125}& {0.5}& {0.375}& {0.5625}\end{array}\right]$ (5)
 > $\mathrm{Tally}\left(C,\mathrm{weights}=W\right)$
 $\left[{1}{=}{0.125000000000000}{,}{3}{=}{0.750000000000000}{,}{\mathrm{π}}{=}{0.562500000000000}{,}{b}{=}{0.375000000000000}{,}{a}{=}{0.500000000000000}\right]$ (6)