1. **State the problem:** We are given a sample data set of hurricane counts: $$20, 19, 17, 15, 3, 16, 15, 9, 19, 11, 2, 7, 12, 18$$ We need to find the sample standard deviation and variance, rounded to one decimal place. 2. **Formulas:** - Sample mean: $$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$ - Sample variance: $$s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$$ - Sample standard deviation: $$s = \sqrt{s^2}$$ 3. **Calculate the mean:** Number of data points: $$n=14$$ Sum: $$20+19+17+15+3+16+15+9+19+11+2+7+12+18=178$$ Mean: $$\bar{x} = \frac{178}{14} = 12.7143$$ 4. **Calculate squared deviations:** Calculate each $$ (x_i - \bar{x})^2 $$: $$(20-12.7143)^2=53.06$$ $$(19-12.7143)^2=39.49$$ $$(17-12.7143)^2=18.37$$ $$(15-12.7143)^2=5.24$$ $$(3-12.7143)^2=94.00$$ $$(16-12.7143)^2=11.22$$ $$(15-12.7143)^2=5.24$$ $$(9-12.7143)^2=13.79$$ $$(19-12.7143)^2=39.49$$ $$(11-12.7143)^2=2.94$$ $$(2-12.7143)^2=114.94$$ $$(7-12.7143)^2=32.63$$ $$(12-12.7143)^2=0.51$$ $$(18-12.7143)^2=27.94$$ Sum of squared deviations: $$= 454.86$$ 5. **Calculate variance:** $$s^2 = \frac{454.86}{14-1} = \frac{454.86}{13} = 34.99$$ 6. **Calculate standard deviation:** $$s = \sqrt{34.99} = 5.92$$ 7. **Round answers:** Variance $$= 35.0$$ Standard deviation $$= 5.9$$ 8. **Answer the conceptual question:** The important feature not revealed by measures of variation is the pattern over time. **Correct choice:** C. The measures of variation reveal nothing about the pattern over time.