Answer :
We are given that the mean of the numbers
[tex]\[
16, \; w, \; 17, \; 9, \; x, \; 2, \; y, \; 7, \; z
\][/tex]
is 11. This means the total sum of the 9 numbers is
[tex]\[
\text{Total Sum} = 11 \times 9 = 99.
\][/tex]
Next, we add the known numbers:
[tex]\[
16 + 17 + 9 + 2 + 7 = 51.
\][/tex]
Since the total sum of all numbers is 99, the sum of the unknown numbers [tex]$w$[/tex], [tex]$x$[/tex], [tex]$y$[/tex], and [tex]$z$[/tex] is
[tex]\[
w + x + y + z = 99 - 51 = 48.
\][/tex]
There are 4 unknown numbers, so the mean of [tex]$w$[/tex], [tex]$x$[/tex], [tex]$y$[/tex], and [tex]$z$[/tex] is
[tex]\[
\text{Mean} = \frac{48}{4} = 12.
\][/tex]
Thus, the mean of [tex]$w$[/tex], [tex]$x$[/tex], [tex]$y$[/tex], and [tex]$z$[/tex] is [tex]$\boxed{12}$[/tex].
[tex]\[
16, \; w, \; 17, \; 9, \; x, \; 2, \; y, \; 7, \; z
\][/tex]
is 11. This means the total sum of the 9 numbers is
[tex]\[
\text{Total Sum} = 11 \times 9 = 99.
\][/tex]
Next, we add the known numbers:
[tex]\[
16 + 17 + 9 + 2 + 7 = 51.
\][/tex]
Since the total sum of all numbers is 99, the sum of the unknown numbers [tex]$w$[/tex], [tex]$x$[/tex], [tex]$y$[/tex], and [tex]$z$[/tex] is
[tex]\[
w + x + y + z = 99 - 51 = 48.
\][/tex]
There are 4 unknown numbers, so the mean of [tex]$w$[/tex], [tex]$x$[/tex], [tex]$y$[/tex], and [tex]$z$[/tex] is
[tex]\[
\text{Mean} = \frac{48}{4} = 12.
\][/tex]
Thus, the mean of [tex]$w$[/tex], [tex]$x$[/tex], [tex]$y$[/tex], and [tex]$z$[/tex] is [tex]$\boxed{12}$[/tex].
