The Mode function computes the mode of a specified random variable or a data sample, and then puts the result into a set. The mode of a set of sample data is the most frequently occurring item in it.

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

If the option output is not included or is specified to be output=value, then the function will return the value of the mode. If output=plot is specified, then the function will return a plot of the input data set and its mode. If output=both is specified, then both the value and the plot of the mode will be returned.

By default, all computations involving random variables are performed symbolically (see option numeric below).

The Mode function selects the values that occur most frequently in the data set. If values appear differently but have the same numeric value, such as $2$, $2.0$, and $\sqrt{4}$, then Mode will consider them equal. If values that appear differently are a mode of the data set, then Mode uses a floating point value equal to that mode if there is one in the data set, or an arbitrarily selected non-floating point value otherwise.

By default, the mode is computed according to the rules mentioned above. To always compute the mode numerically, specify the numeric or numeric = true option.

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

$\mathrm{Mode}\left(\mathrm{BinomialRandomVariable}\left(p\,q\right)\right)$

$\left\{\begin{array}{cc}\left\{0\right\}& q=0\\ \left\{p\right\}& q=1\\ \left\{\left(1+p\right)q\,\left(1+p\right)q-1\right\}& \left(\left(1+p\right)q\right)::\mathbb{Z}\\ \left\{⌊\left(1+p\right)q⌋\right\}& \mathrm{otherwise}\end{array}\right.$

$\mathrm{Mode}\left(\mathrm{BinomialRandomVariable}\left(20\,0.6\right)\right)$

$\left\{12\right\}$

$A≔⟨1\,2\,2\,2\,2\,2\,3\,4\,5\,5\,5\,6\,7\,7\,7\,7.0\,7\,7\,8\,8\,1\,1\,2\,3\,4\,5⟩\:$

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

$\left\{2\,7.0\right\}$

$\mathrm{Mode}\left(A\,\mathrm{numeric}\right)$

$\left\{2.\,7.0\right\}$

$\mathrm{Mode}\left(A\,\mathrm{output}=\mathrm{plot}\right)$

$M≔\mathrm{Matrix}\left(\left[\left[3\,\mathrm{\pi }\,4\right]\,\left[4\,\mathrm{\pi }\,4\right]\,\left[3.0\,3.1415926\,4\right]\,\left[2\,1\,10\right]\,\left[4\,110\,\mathrm{sqrt}\left(2\right)\right]\right]\right)$

$M≔\left[\right]$

$\mathrm{Mode}\left(M\right)$

$\mathrm{mode},\mathrm{graph}≔\mathrm{Mode}\left(M\,\mathrm{output}=\mathrm{both}\right)$

$\mathrm{mode},\mathrm{graph}≔\left[?\right],$

$\mathrm{mode}$

$\mathrm{graph}$

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

The Student[Statistics][Mode] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.