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.

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.

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

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

$A≔\mathrm{Array}\left(\left[3\,3\,3\,1\,1\,a\,b\,b\,a\,a\,a\,a\,\mathrm{\pi }\,\mathrm{\pi }\,\mathrm{\pi }\,\mathrm{\pi }\right]\right)$

$A≔\left[\begin{array}{cccccccccccccccc}3& 3& 3& 1& 1& a& b& b& a& a& a& a& \mathrm{\pi }& \mathrm{\pi }& \mathrm{\pi }& \mathrm{\pi }\end{array}\right]$

$\mathrm{Tally}\left(A\right)$

$\left[1=2\,\mathrm{\pi }=4\,3=3\,a=5\,b=2\right]$

$\mathrm{Tally}\left(A\,\mathrm{output}=\mathrm{table}\right)$

$table\left(\left[1=2\,\mathrm{\pi }=4\,3=3\,a=5\,b=2\right]\right)$

$C≔\mathrm{Array}\left(\left[3\,3\,1\,a\,b\,\mathrm{\pi }\right]\right)$

$C≔\left[\begin{array}{cccccc}3& 3& 1& a& b& \mathrm{\pi }\end{array}\right]$

$W≔\mathrm{Array}\left(\left[0.25\,0.5\,0.125\,0.5\,0.375\,0.5625\right]\right)$

$W≔\left[\begin{array}{cccccc}0.25& 0.5& 0.125& 0.5& 0.375& 0.5625\end{array}\right]$

$\mathrm{Tally}\left(C\,\mathrm{weights}=W\right)$

$\left[1=0.125000000000000\,\mathrm{\pi }=0.562500000000000\,3=0.750000000000000\,a=0.500000000000000\,b=0.375000000000000\right]$