What is the (population) **standard deviation** of the five numbers $0$, $7$, $8$, $10$, and $10$, rounded to one decimal place?

Five steps: 1. **Mean.** $\dfrac{0 + 7 + 8 + 10 + 10}{5} = \dfrac{35}{5} = 7$. 2. **Differences from mean.** $0 - 7 = -7$, $7 - 7 = 0$, $8 - 7 = 1$, $10 - 7 = 3$, $10 - 7 = 3$. 3. **Square the differences.** $49, 0, 1, 9, 9$. 4. **Average of the squared differences (the *variance*).** $\dfrac{49 + 0 + 1 + 9 + 9}{5} = \dfrac{68}{5} = 13.6$. 5. **Take the square root.** $\sqrt{13.6} \approx 3.7$. So the population standard deviation is $\approx 3.7$. - **D** ($13.6$) is the variance — the step *before* taking the square root. A frequent trap. - **C** ($5.0$) is roughly the range divided by 2, which is not a standard formula. - **A** ($1.6$) is too small for data spanning 0 to 10.