  In this article we study the braid indices of 2-bridge knots with a fixed
crossing number $c$. We show that the average braid index of the set of
$2$-bridge knots of crossing number $c$ is asymptotically linear, approaching
$\frac{c}{3}+\frac{11}{9}$. Additionally, we show that the variance of the
braid indices of the set of $2$-bridge knots of crossing number $c$ is also
asymptotically linear, approaching $\frac{2c}{27} - \frac{10}{81}$. Finally, we
find a formula for the number $k_{c,b}$ of $2$-bridge knots with crossing
number $c$ and braid index $b$, and show that for any fixed $c$, the braid
index where $k_{c,b}$ achieves its maximum is $b=\left\lceil
\frac{c}{3}\right\rceil +1$.
