Variability of an estimator

Variability describes the spread of an estimator's sampling distribution, so low variability means two different samples would hand you nearly the same answer. It is a separate goal from low bias: an estimator can be centered correctly and still swing wildly, or be very consistent and consistently wrong. Larger samples cut variability, and the square root sets the pace: with $p = 0.5$, $n = 100$ gives $\sqrt{\frac{0.5(0.5)}{100}} = \sqrt{0.0025} = 0.05$, while $n = 400$ gives $\sqrt{\frac{0.25}{400}} = \sqrt{0.000625} = 0.025$. Only a better sampling design fixes bias.