Chapter 15, Problem 74E

Suppose that the standard deviation of the data set $\{x_1,x_2,x_3,\mathrm{......}{x}_N$ is $\sigma$. Explain why the standard deviation of the data set $\left\{a\cdot x_1,a\cdot x_2,a\cdot x_3,\mathrm{.....}a\cdot x_N\right\}$ (where $a$ is a positive number) is $a\cdot \sigma$.