1. **State the problem:** We need to find the range, variance, and standard deviation of the starting salaries for 7 states: Washington (30974), Wisconsin (25222), Colorado (35086), Vermont (26461), Rhode Island (33815), Michigan (35557), Indiana (30844). 2. **Find the range:** The range is the difference between the maximum and minimum values. Maximum salary = 35557 (Michigan) Minimum salary = 25222 (Wisconsin) Range = $35557 - 25222 = 10335$ 3. **Find the variance:** Variance formula for a sample is $$s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$$ where $n=7$ and $\bar{x}$ is the mean. Calculate the mean: $$\bar{x} = \frac{30974 + 25222 + 35086 + 26461 + 33815 + 35557 + 30844}{7} = \frac{217959}{7} = 31137$$ Calculate each squared deviation: $(30974 - 31137)^2 = (-163)^2 = 26569$ $(25222 - 31137)^2 = (-5915)^2 = 34987225$ $(35086 - 31137)^2 = 3949^2 = 15592701$ $(26461 - 31137)^2 = (-4676)^2 = 21867576$ $(33815 - 31137)^2 = 2678^2 = 7178884$ $(35557 - 31137)^2 = 4420^2 = 19536400$ $(30844 - 31137)^2 = (-293)^2 = 85849$ Sum of squared deviations: $$26569 + 34987225 + 15592701 + 21867576 + 7178884 + 19536400 + 85849 = 99133604$$ Variance: $$s^2 = \frac{99133604}{7-1} = \frac{99133604}{6} = 16522267.3$$ 4. **Find the standard deviation:** It is the square root of the variance. $$s = \sqrt{16522267.3} \approx 4064.3$$ **Final answers:** Range = 10335 Variance = 16522267.3 Standard deviation = 4064.3