Assume we have two N$-$point discrete sequences, $x(n)$ and $y(n),$ where n goes from $1nN,$ and the N$-$point averages of the two sequences are

$x_{\text{a}\text{v}\text{e}}=\frac{1}{N}{\displaystyle \underset{n=1}{\overset{N}{}}}x(n),$ and $y_{\text{a}\text{v}\text{e}}=\frac{1}{N}{\displaystyle \underset{n=1}{\overset{N}{}}}y(n)$

Next let's add the two sequences, element by element, to get a new N $-$point discrete sequence $z(n)=x(n)+y(n).$ Then would it be correct to say that the average of