Below is the graph of an ellipse. (Assume that tick marks are placed every $1$ unit along the axes.) Compute the coordinates of the focus of the ellipse with the greater $x$-coordinate.
The center of the ellipse with tick marks every unit is $\left( \frac{11}{2}, 3 \right).$ For the crests and endpoints of the major and minor axes, we have the values in the table below.
\[\begin{array}{c|c|c} & x & y \\ \hline \text{Crest of major axis} & 9 & 3 \\ \text{Endpoint of major axis} & 6.5 & 3 \\ \text{Crest of minor axis} & 5.5 & 4 \\ \text{Endpoint of minor axis} & 5.5 & 2 \end{array}\]From this information, we can see that the ellipse is wider than it is tall. Therefore, the ellipse is longer along the $x$-axis, and its focus with greater $x$-coordinate will be closer to its center than its focus with smaller $x$-coordinate.
Since the center is $\left( \frac{11}{2}, 3 \right),$ the focus with greater $x$-coordinate is $\boxed{\left( \frac{9}{4}, 3 \right)}.$
[asy]
unitsize(0.4 cm);
real ellipse (real x) {
return(1.5*sqrt(1 - (x^2)/49));
}
draw(shift((0,-6))*(graph(ellipse,-9.4,9.4)),red);
draw(ellipse(0)^^ellipse(5.5));
dot("$(6.5,3)$", (6.5,3), E);
dot("$(5.5,4)$", (5.5,4), NW);
dot("$(5.5,2)$", (5.5,2), SW);
dot("$(9,3)$", (9,3), N);
dot("$(11/2,3)$", (11/2,3), NE);
dot("$(9/4,3)$", (9/4,3), E);
dot((11/2,3));
[/asy]