1. Problem 1: Frog lengths data: 7.3, 8.1, 7.8, 8.4, 7.9, 8.2, 7.6, 8.0, 7.7 2. (a) Range = max - min = 8.4 - 7.3 = $1.1$ 3. (b) Ordered data: 7.3, 7.6, 7.7, 7.8, 7.9, 8.0, 8.1, 8.2, 8.4 4. First quartile $Q_1$ is the median of first 4 values: median of (7.3, 7.6, 7.7, 7.8) = $\frac{7.6+7.7}{2} = 7.65$ 5. Third quartile $Q_3$ is median of last 4 values: median of (8.0, 8.1, 8.2, 8.4) = $\frac{8.1+8.2}{2} = 8.15$ 6. Interquartile range $IQR = Q_3 - Q_1 = 8.15 - 7.65 = 0.5$ 7. (c) Sample variance: $\bar{x} = \frac{7.3+8.1+7.8+8.4+7.9+8.2+7.6+8.0+7.7}{9} = \frac{70}{9} \approx 7.778$ 8. Sum of squared deviations: $\sum (x_i - \bar{x})^2 =$ $(7.3-7.778)^2 + (8.1-7.778)^2 + ... + (7.7-7.778)^2 \approx 1.047$ 9. Sample variance $s^2 = \frac{1.047}{9-1} = \frac{1.047}{8} \approx 0.131$ 10. (d) Sample standard deviation $s = \sqrt{0.131} \approx 0.362$ 11. Problem 2: Test scores: 42, 45, 39, 47, 44, 41, 46, 40, 43, 48, 44, 42 12. (a) Range = max - min = 48 - 39 = $9$ 13. (b) Ordered: 39, 40, 41, 42, 42, 43, 44, 44, 45, 46, 47, 48 14. $Q_1$ median lower half (first 6): median between 41 and 42 = $\frac{41+42}{2} = 41.5$ 15. $Q_3$ median upper half (last 6): median between 45 and 46 = $\frac{45+46}{2} = 45.5$ 16. $IQR = Q_3 - Q_1 = 45.5 - 41.5 = 4$ 17. (c) Mean $\bar{x} = \frac{42+45+39+47+44+41+46+40+43+48+44+42}{12} = \frac{521}{12} \approx 43.42$ 18. Sum squared deviations $\approx 105.92$ 19. Sample variance $s^2 = \frac{105.92}{12-1} = \frac{105.92}{11} \approx 9.63$ 20. (d) Sample standard deviation $s = \sqrt{9.63} \approx 3.1$ 21. Problem 3: Thickness data: 1.12, 1.09, 1.15, 1.11, 1.14, 1.10, 1.13, 1.08, 1.16, 1.07 22. (a) Range = max - min = 1.16 - 1.07 = $0.09$ 23. (b) Ordered: 1.07, 1.08, 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16 24. $Q_1$ median lower half (first 5): median is 1.09 25. $Q_3$ median upper half (last 5): median is 1.14 26. $IQR = 1.14 - 1.09 = 0.05$ 27. (c) Mean $\bar{x} = \frac{\sum x_i}{10} = \frac{11.15}{10} = 1.115$ 28. Sum squared deviations $\approx 0.00685$ 29. Sample variance $s^2 = \frac{0.00685}{9} \approx 0.000761$ 30. (d) Sample standard deviation $s = \sqrt{0.000761} \approx 0.0276$