The Mean function computes and/or plots the arithmetic mean of the specified random variable or data set. This is the same as the expected value of the random variable. The same command can be obtained as  ExpectedValue.

The first parameter can be a data sample (e.g., a Vector), a Matrix data set, 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 mean. If output=plot is specified, then the function will return a plot of the input data set and its mean. If output=both is specified, then both the value and the plot of the mean will be returned.

If the option inert is not included or is specified to be inert=false, then the function will return the actual value of the result. If inert or inert=true is specified, then the function will return the formula of evaluating the actual value.

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

If there are floating point values or the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.

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

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

$\mathrm{Mean}\left(\left[2\,4\,4.0\right]\right)$

$3.333333333$

$\mathrm{Mean}\left(\mathrm{Vector}\left[\mathrm{column}\right]\left(\left[\mathrm{sqrt}\left(14.0\right)\,\mathrm{\pi }\,33\right]\right)\right)$

$13.29441668$

$\mathrm{Mean}\left(\left[2\,4\,4\right]\right)$

$\frac{10}{3}$

$\mathrm{Mean}\left(\left[100\,20\,\mathrm{\pi }\right]\right)$

$40+\frac{\mathrm{\pi }}{3}$

$\mathrm{Mean}\left(\mathrm{Vector}\left[\mathrm{row}\right]\left(\left[\mathrm{sqrt}\left(2\right)\,3\,\mathrm{\pi }\right]\right)\right)$

$1+\frac{\sqrt{2}}{3}+\frac{\mathrm{\pi }}{3}$

$\mathrm{Mean}\left(\mathrm{BetaRandomVariable}\left(p\,q\right)\right)$

$\frac{p}{p+q}$

$\mathrm{Mean}\left(\mathrm{BetaRandomVariable}\left(3\,5\right)\right)$

$\frac{3}{8}$

$\mathrm{Mean}\left(\mathrm{BetaRandomVariable}\left(3\,5\right)\,\mathrm{numeric}\right)$

$0.3750000000$

$\mathrm{Mean}\left(\mathrm{BetaRandomVariable}\left(3\,5\right)\,\mathrm{inert}\right)$

${\int }_0^{1}105{\mathrm{\_t}}^3{\left(1-\mathrm{\_t}\right)}^4\ⅆ\mathrm{\_t}$

$\mathrm{evalf}\left(\mathrm{Mean}\left(\mathrm{BetaRandomVariable}\left(3\,5\right)\,\mathrm{inert}\right)\right)$

$0.3750000000$

$\mathrm{Mean}\left(\mathrm{BetaRandomVariable}\left(3\,5\right)\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{Mean}\left(\left[x\,y\,z\right]\right)$

$\frac{x}{3}+\frac{y}{3}+\frac{z}{3}$

$M≔\mathrm{Matrix}\left(\left[\left[2.0\,7.5\,10\,18\right]\,\left[3\,5\ln \left(2\right)\,1\,\mathrm{\pi }\right]\,\left[4\,2\,7\,4\right]\right]\right)$

$M≔\left[\begin{array}{cccc}2.0& 7.5& 10& 18\\ 3& 5\ln \left(2\right)& 1& \mathrm{\pi }\\ 4& 2& 7& 4\end{array}\right]$

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

$\left[\begin{array}{cccc}3.000000000& 4.321911968& 6& \frac{22}{3}+\frac{\mathrm{\pi }}{3}\end{array}\right]$

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

$\left[\begin{array}{cccc}3.000000000& 4.321911968& 6& \frac{22}{3}+\frac{\mathrm{\pi }}{3}\end{array}\right]$

$\mathrm{Mean}\left(\left[1\,2\,3\,4\right]\,\mathrm{numeric}\right)$

$2.50000000000000$

$\mathrm{mean},\mathrm{graph}≔\mathrm{Mean}\left(\left[1\,2\,3\,4\right]\,\mathrm{numeric}\,\mathrm{output}=\mathrm{both}\right)$

$\mathrm{mean},\mathrm{graph}≔2.50000000000000,\mathrm{PLOT}\left(\mathrm{...}\right)$

$\mathrm{mean}$

$2.50000000000000$

$\mathrm{graph}$

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

The Student[Statistics][Mean] and Student[Statistics][ExpectedValue] commands were introduced in Maple 18.

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