1. **State the problem:** Find the standard deviation of the set $S = \{1,2,6,7,3,15,10,18,5\}$. 2. **Formula:** The standard deviation $\sigma$ for a sample is given by: $$\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^n (x_i - \mu)^2}$$ where $n$ is the number of elements and $\mu$ is the mean of the set. 3. **Calculate the mean $\mu$:** $$\mu = \frac{1+2+6+7+3+15+10+18+5}{9} = \frac{67}{9} \approx 7.444$$ 4. **Calculate each squared deviation $(x_i - \mu)^2$:** - $(1 - 7.444)^2 = 41.493$ - $(2 - 7.444)^2 = 29.645$ - $(6 - 7.444)^2 = 2.086$ - $(7 - 7.444)^2 = 0.197$ - $(3 - 7.444)^2 = 19.753$ - $(15 - 7.444)^2 = 57.006$ - $(10 - 7.444)^2 = 6.528$ - $(18 - 7.444)^2 = 111.111$ - $(5 - 7.444)^2 = 5.975$ 5. **Sum the squared deviations:** $$41.493 + 29.645 + 2.086 + 0.197 + 19.753 + 57.006 + 6.528 + 111.111 + 5.975 = 273.794$$ 6. **Calculate the variance:** $$\text{variance} = \frac{273.794}{9} = 30.421$$ 7. **Calculate the standard deviation:** $$\sigma = \sqrt{30.421} \approx 5.52$$ **Final answer:** The standard deviation of the set $S$ is approximately $5.52$.