1. **State the problem:** Calculate the value of $$\sqrt{\frac{1}{5} \cdot \left((18 - 8.6)^2 + (4 - 8.6)^2 + (16 - 8.6)^2 + (5 - 8.6)^2 + (0 - 8.6)^2\right)}$$. 2. **Formula and explanation:** This expression calculates the standard deviation of the data set $\{18, 4, 16, 5, 0\}$ with mean 8.6. The formula for standard deviation is $$\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2}$$ where $n=5$ and $\mu=8.6$. 3. **Calculate each squared difference:** $$ (18 - 8.6)^2 = (9.4)^2 = 88.36 $$ $$ (4 - 8.6)^2 = (-4.6)^2 = 21.16 $$ $$ (16 - 8.6)^2 = (7.4)^2 = 54.76 $$ $$ (5 - 8.6)^2 = (-3.6)^2 = 12.96 $$ $$ (0 - 8.6)^2 = (-8.6)^2 = 73.96 $$ 4. **Sum the squared differences:** $$ 88.36 + 21.16 + 54.76 + 12.96 + 73.96 = 251.2 $$ 5. **Divide by the number of data points (5):** $$ \frac{251.2}{5} = 50.24 $$ 6. **Take the square root:** $$ \sqrt{50.24} \approx 7.09 $$ **Final answer:** The value of the expression is approximately **7.09**.