1. **State the problem:** Calculate the variance and standard deviation for the sample data: 10, 7, 9, 1, 2, 0, 6. 2. **Recall the formulas:** - Sample variance: $$s^2 = \frac{ss}{n-1}$$ - Sum of squares: $$ss = \sum x^2 - \frac{(\sum x)^2}{n}$$ 3. **Given values:** - $$\sum x = 35$$ - $$\sum x^2 = 271$$ - Sample size $$n = 7$$ 4. **Calculate sum of squares (ss):** $$ss = 271 - \frac{35^2}{7} = 271 - \frac{1225}{7} = 271 - 175 = 96$$ 5. **Calculate variance:** $$s^2 = \frac{ss}{n-1} = \frac{96}{7-1} = \frac{96}{6} = 16$$ 6. **Calculate standard deviation:** $$s = \sqrt{s^2} = \sqrt{16} = 4$$ **Final answers:** - Variance $$s^2 = 16$$ - Standard deviation $$s = 4$$