Question

what happens to the standard deviation when you double the number?

Answer 1

double which number?
A standard deviation has the following equation:
\[\sigma=\sqrt{(1/N)*\sum_{i=1}^{N} (x _{i}-\mu)^2}\]

Answer 2

Where N is the population size... so I would say if N is the number that is being doubled, play around with the equation a few times and see what happens to the standard deviation