The Mean(A) command returns the mean of the Array $A$, defined as

where $N$ is the number of elements of $A$. When an Array $W$ for weights of size $N$ is provided, the mean is defined instead as

with $\mathrm{Mean}\left(A\,W\right)=\mathrm{Mean}\left(A\right)$ when $W_k=\frac{1}{N}$.

The StandardDeviation(B) command returns the standard deviation of the Array $B$, defined as

where $N$ is the number of elements of $B$, and $\mathrm{\mu }$ is the mean of $B$.

The MeanStandardDeviation(B) command computes the mean and standard deviation of $B$ simultaneously, and returns an expression sequence consisting of these values, respectively.

The Mean, StandardDeviation, and MeanStandardDeviation commands also accept lists and other types of rtables, both one-dimensional and multi-dimensional, which are then converted to 1-D Arrays.

For all of these commands, Maple may convert the input signal. Before the code performing Mean runs, Maple converts $A$ to a hardware datatype, first attempting float[8] and subsequently complex[8], unless it already has one of these datatypes. Similarly, before the code performing StandardDeviation or MeanStandardDeviation runs, $B$ is converted to datatype float[8] if it does not have that datatype already. For this reason, it is most efficient if the input Array has an appropriate datatype already.

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

$a≔\mathrm{Array}\left(\left[1\,2\,3\,4\,5\right]\,'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\right)$

$a≔\left[\begin{array}{ccccc}1.& 2.& 3.& 4.& 5.\end{array}\right]$

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

$3.$

$w≔\mathrm{Array}\left(\left[5\,4\,3\,2\,1\right]\,'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\right)$

$w≔\left[\begin{array}{ccccc}5.& 4.& 3.& 2.& 1.\end{array}\right]$

$\mathrm{Mean}\left(a\,w\right)$

$2.33333333333333348$

$\mathrm{StandardDeviation}\left(a\right)$

$1.58113883008418976$

$\mathrm{MeanStandardDeviation}\left(a\right)$

$3.,1.58113883008418976$

The SignalProcessing[Mean], SignalProcessing[StandardDeviation] and SignalProcessing[MeanStandardDeviation] commands were introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.

The SignalProcessing[Mean], SignalProcessing[StandardDeviation] and SignalProcessing[MeanStandardDeviation] commands were updated in Maple 2021.