Data & Statistics · Challenge problem

The data set $2,\ 4,\ 5,\ 7,\ 8,\ 9,\ 11,\ v$ has $v$ as its largest value. Using $Q_1$ and $Q_3$ as the medians of the lower and upper halves, and calling a value an outlier when it is more than $1.5\times\text{IQR}$ above $Q_3$, what is the smallest whole number $v$ that is an outlier?