When we want to find the standard deviation of $\{1,2,2,3,5\}$ we do

$$\sigma = \sqrt{ {1 \over 5-1} \left( (1-2.6)^2 + (2-2.6)^2 + (2-2.6)^2 + (3-2.6)^2 + (5 - 2.6)^2 \right) } \approx 1.52$$.

Why do we need to square and then square-root the numbers?