1. **State the problem:** We are given a sample of scores: 1, 3, 1, 1. We need to calculate the sum of squares (SS) using the computational formula, then compute the sample variance and standard deviation. 2. **Recall the formulas:** - Sum of squares (SS) using computational formula: $$SS = \sum x_i^2 - \frac{(\sum x_i)^2}{n}$$ - Sample variance: $$s^2 = \frac{SS}{n-1}$$ - Sample standard deviation: $$s = \sqrt{s^2}$$ 3. **Calculate the sums:** - $$\sum x_i = 1 + 3 + 1 + 1 = 6$$ - $$\sum x_i^2 = 1^2 + 3^2 + 1^2 + 1^2 = 1 + 9 + 1 + 1 = 12$$ - Sample size $$n = 4$$ 4. **Calculate SS:** $$SS = 12 - \frac{6^2}{4} = 12 - \frac{36}{4} = 12 - 9 = 3$$ 5. **Calculate sample variance:** $$s^2 = \frac{SS}{n-1} = \frac{3}{4-1} = \frac{3}{3} = 1$$ 6. **Calculate sample standard deviation:** $$s = \sqrt{1} = 1$$ **Final answers:** - Sum of squares (SS) = 3 - Sample variance = 1 - Sample standard deviation = 1