For a binomial distribution with $n = 16$, what is the largest possible variance?

Explanation

1. 01

   $npq = 16p(1 - p)$, and $p(1 - p)$ is largest at $p = \frac{1}{2}$, where it is $\frac{1}{4}$.

2. 02

   Largest variance $= 16 \times \frac{1}{4} = 4$.