1. **Problem:** Find the standard deviation of the data set: 20, 25, 30, 36, 32, 43. 2. **Formula:** The standard deviation $\sigma$ for a sample is given by: $$\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})^2}$$ where $n$ is the number of observations, $x_i$ are the data points, and $\bar{x}$ is the mean. 3. **Step 1: Calculate the mean $\bar{x}$** $$\bar{x} = \frac{20 + 25 + 30 + 36 + 32 + 43}{6} = \frac{186}{6} = 31$$ 4. **Step 2: Calculate each squared deviation $(x_i - \bar{x})^2$** - $(20 - 31)^2 = (-11)^2 = 121$ - $(25 - 31)^2 = (-6)^2 = 36$ - $(30 - 31)^2 = (-1)^2 = 1$ - $(36 - 31)^2 = 5^2 = 25$ - $(32 - 31)^2 = 1^2 = 1$ - $(43 - 31)^2 = 12^2 = 144$ 5. **Step 3: Sum the squared deviations** $$121 + 36 + 1 + 25 + 1 + 144 = 328$$ 6. **Step 4: Calculate variance** $$\text{variance} = \frac{328}{6} = 54.67$$ 7. **Step 5: Calculate standard deviation** $$\sigma = \sqrt{54.67} \approx 7.39$$ **Final answer:** The standard deviation of the data set is approximately $7.39$.