The standard deviation of a data set is approximately $3.7$. If every value in the data set is **doubled**, what happens to the standard deviation of the new data set?

If every value $x_i$ is multiplied by $k$, then every deviation $(x_i - \bar x)$ is also multiplied by $k$, every squared deviation by $k^2$, and the variance by $k^2$. Therefore the **standard deviation** (square root of variance) is multiplied by $|k|$. With $k = 2$: new SD $= 2 \times 3.7 = 7.4$. - Trap D quadruples — that's what happens to **variance**, not SD. - Trap A would be true if you *added* a constant, not *multiplied*.